the global cauchy problem for the nls and nlkg with small rough data abstract by using the unit cube decomposition to the frequency spaces we study the cauchy problem for the nonlinear schrodinger equation and the nonlinear klein gordon equation some global well posedness results are obtained for the small cauchy data in some modulation spaces m p 1 s

a unifying framework for adaptive radar detection in homogeneous plus structured interference part i on the maximal invariant statistic this paper deals with the problem of adaptive multidimensional multichannel signal detection in homogeneous gaussian disturbance with unknown covariance matrix and structured deterministic interference the aforementioned problem corresponds to a generalization of the well known generalized multivariate analysis of variance gmanova in this part i of the paper we formulate the considered problem in canonical form and after identifying a desirable group of transformations for the considered hypothesis testing we derive a maximal invariant statistic mis for the problem at hand furthermore we provide the mis distribution in the form of a stochastic representation finally strong connections to the mis obtained in the open literature in simpler scenarios are underlined

time frequency analysis of localization operators abstract we study a class of pseudodifferential operators known as time frequency localization operators anti wick operators gabor toeplitz operators or wave packets given a symbol a and two windows 1 2 we investigate the multilinear mapping from a 1 2 s r 2d s r d s r d to the localization operator aa 1 2 and we give sufficient and necessary conditions for aa 1 2 to be bounded or to belong to a schatten class our results are formulated in terms of time frequency analysis in particular we use modulation spaces as appropriate classes for symbols and windows

weighted modulation space mp qs w with w a loc abstract in the present paper we present a natural extension of the modulation spaces m p q s with 0 p 0 q and s r the weight we take up here belongs to the class a loc which is even wider and contains weights of exponential growth after defining the function spaces we investigate their atomic and molecular decomposition as well as some elementary properties

metaplectic representation on wiener amalgam spaces and applications to the schrodinger equation we study the action of metaplectic operators on wiener amalgam spaces giving upper bounds for their norms as an application we obtain new fixed time estimates in these spaces for schrodinger equations with general quadratic hamiltonians and strichartz estimates for the schrodinger equation with potentials v x x 2

estimate for generalized unimodular multipliers on modulation spaces abstract in this paper we consider the operator e i t h d where h defined on r n is a c r n 0 positive homogeneous function with degree 0 and r r is a smooth function satisfying the following a1 there exists a constant m 1 0 such that for all n 0 n 0 r r m 1 r 1 a2 there exists a constant m 2 0 such that for all n 0 r r m 2 0 r 1 we prove the boundedness of the operator e i t h d on the modulation spaces and obtain its asymptotic estimate as t goes to infinity as applications we give the grow up rate of the solutions for the cauchy problems for the generalized wave klein gordon and schrodinger equations

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

adaptive array detection of uncertain rank one waveforms adaptive array detection of known within a complex scaling rank one space time waveforms in unknown spatial noise has received considerable attention the two published solutions are the adaptive matched filter and the glrt we expand on this work to consider the case of rank one waveforms that are uncertain i e only partially known more precisely we model the space time steering vector as the kronecker product of two vectors each of which is unknown but is known to lie in a known subspace applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication using the principle of invariance we construct detectors based on the maximal invariant we show that the snr required to achieve a given detection probability for a given false alarm rate is only weakly impacted by waveform uncertainty thus our detector approaches the performance of earlier detectors which entail known waveforms

on the statistical invariance for adaptive radar detection in partially homogeneous disturbance plus structured interference this paper deals with the problem of adaptive vector subspace signal detection in partially homogeneous gaussian disturbance and structured unknown deterministic interference within the framework of invariance theory it is first proved that the maximal invariant statistic mis for the problem at hand is scalar valued and coincides with the well known adaptive normalized matched filter evaluated after data projection in the complementary subspace of the interfering signal second the statistical characterization of the mis under both hypotheses is derived then it is shown the statistical equivalence of two step generalized likelihood ratio test rao and wald tests as well as the more recently considered durbin and gradient test to the above statistic finally simulation results are provided to confirm our findings and analyze the performance trend of the mis with the relevant parameters

decay and smoothness for eigenfunctions of localization operators abstract we study decay and smoothness properties for eigenfunctions of compact localization operators a a 1 2 operators a a 1 2 with symbols a in the wide modulation space m p containing the lebesgue space l p p and windows 1 2 in the schwartz class s are known to be compact we show that their l 2 eigenfuctions with non zero eigenvalues are indeed highly compressed onto a few gabor atoms similarly for symbols a in the weighted modulation spaces m v s 1 r 2 d s 0 subspaces of m p r 2 d p 2 d s the l 2 eigenfunctions of a a 1 2 are actually schwartz functions an important role is played by quasi banach wiener amalgam and modulation spaces as a tool new convolution relations for modulation spaces and multiplication relations for wiener amalgam spaces in the quasi banach setting are exhibited

on the l2 boundedness of pseudo differential operators and their commutators with symbols in α modulation spaces abstract the results of sjostrand j sjostrand an algebra of pseudodifferential operators math res lett 1 1994 185 192 and sugimoto m sugimoto l p boundedness of pseudo differential operators satisfying besov estimates i j math soc japan 40 1988 105 122 on a mapping property of pseudo differential operators are two different kinds of extensions of the pioneering work by calderon and vaillancourt a p calderon r vaillancourt on the boundedness of pseudo differential operators j math soc japan 23 1971 374 378 the objective of this paper is to show that these two results which appeared to be independent ones can be proved based on the same principle for the purpose we use the modulation spaces a parameterized family of function spaces which include besov spaces and modulation spaces as special cases as an application we also discuss the l 2 boundedness of the commutator x d a where a x is a lipschitz function and belongs to an modulation space

closed loop problems in biomechanics part ii an optimization approach abstract a closed loop problem in biomechanics may be defined as a problem in which there are one or more closed loops formed by the human body in contact with itself or with an external system under certain conditions the problem is indeterminate the unknown forces and torques outnumber the equations force transducing devices which would help solve this problem have serious drawbacks and existing methods are inaccurate and non general the purposes of the present paper are 1 to develop a general procedure for solving closed loop problems 2 to illustrate the application of the procedure and 3 to examine the validity of the procedure a mathematical optimization approach is applied to the solution of three different closed loop problems walking up stairs vertical jumping and cartwheeling the following conclusions are drawn 1 the method described is reasonably successful for predicting horizontal and vertical reaction forces at the distal segments although problems exist for predicting the points of application of these forces 2 the results provide some support for the notion that the human neuromuscular mechanism attempts to minimize the joint torques and thus to a certain degree the amount of muscular effort 3 in the validation procedure it is desirable to have a force device for each of the distal segments in contact with a fixed external system and 4 the method is sufficiently general to be applied to all classes of closed loop problems

uncertainty principle positivity and lp boundedness for generalized spectrograms abstract in this paper we are concerned with the properties of positivity uncertainty principle and continuity in l p spaces of a generalized spectrogram in particular we study the connections of a generalized spectrogram as a subclass of the cohen class with the rihaczek and the wigner representations we also consider the behavior of the generalized spectrogram with respect to the positivity and the l p boundedness of the corresponding localization operators

ill posedness for a system of quadratic nonlinear schrodinger equations in two dimensions abstract this paper concerns the ill posedness issue for a system of quadratic nonlinear schrodinger equations in two dimensions from previous studies for the large time behavior of the solution to the system one may expect that the critical regularity to show the well posedness depends on the dispersion coefficients to prove the ill posedness we show the failure of the uniform continuity of the data solution map for the mass resonance case and show the norm inflation for other cases

modulation spaces and non linear hartree type equations abstract we study the cauchy problem for hartree equation with cubic convolution nonlinearity f u k u 2 u under a specified condition on potential k with cauchy data in modulation spaces m p q r n we establish global well posedness results in m p p r n with 1 p 2 n n when k x x r 0 m i n 2 n 2 in m p q r n with 1 q p 2 when k m 1 r n

time frequency analysis of born jordan pseudodifferential operators abstract born jordan operators are a class of pseudodifferential operators arising as a generalization of the quantization rule for polynomials on the phase space introduced by born and jordan in 1925 the weak definition of such operators involves the born jordan distribution first introduced by cohen in 1966 as a member of the cohen class we perform a time frequency analysis of the cohen kernel of the born jordan distribution using modulation and wiener amalgam spaces we then provide sufficient and necessary conditions for born jordan operators to be bounded on modulation spaces we use modulation spaces as appropriate symbols classes

ill posedness for the navier stokes equations in critical besov spaces b q 1 abstract we study the cauchy problem for the incompressible navier stokes equations in two and higher spatial dimensions 0 1 u t u u u p 0 div u 0 u 0 x u 0 for arbitrarily small 0 we show that the solution map u 0 u in critical besov spaces b q 1 q 1 2 is discontinuous at origin it is known that the navier stokes equation is globally well posed for small data in bmo 1 20 taking notice of the embedding b q 1 bmo 1 q 2 we see that for sufficiently small 0 u 0 b q 1 q 2 can guarantee that 0 1 has a unique global solution in bmo 1 however this solution is instable in b q 1 and the solution can have an inflation in b q 1 for certain initial data

adaptive detection in gaussian interference with unknown covariance after reduction by invariance in this paper we address the problem of adaptive detection in homogeneous gaussian interference with unknown covariance matrix after reduction by invariance starting from a maximal invariant statistic which contains all the information for the synthesis of an invariant detector we devise the rao test generalized likelihood ratio test glrt and durbin test moreover we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data i e before reduction by invariance we prove that the glrt in the original data space is statistically equivalent to the glrt designed after reduction by invariance under a very mild assumption and coincide with the conditional uniformly most powerful invariant c umpi test obtained conditioning on an ancillary part of the maximal invariant statistic as to the rao and durbin criteria when they are applied after reduction by invariance lead to detectors different from the counterparts devised in the raw data domain at the analysis stage the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations

time frequency representations of wigner type and pseudo differential operators we introduce a dependent wigner representation wig e 0 1 which permits us to define a general theory connecting time frequency representations on one side and pseudo differential operators on the other the scheme includes various types of time frequency representations among the others the classical wigner and rihaczek representations and the most common classes of pseudo differential operators we show further that the integral over t of wig yields a new representation q possessing features in signal analysis which considerably improve those of the wigner representation especially for what concerns the so called ghost frequencies the relations of all these representations with respect to the generalized spectrogram and the cohen class are then studied furthermore a characterization of the l p boundedness of both pseudo differential operators and t wigner representations are obtained

adaptive beamformer orthogonal rejection test research in the area of signal detection in the presence of unknown interference has resulted in a number of adaptive detection algorithms examples of such algorithms include the adaptive matched filter amf the generalized likelihood ratio test glrt and the adaptive coherence estimator ace each of these algorithms results in a tradeoff between detection performance for matched signals and rejection performance for mismatch signals this paper introduces a new detection algorithm we call the adaptive beamformer orthogonal rejection test abort our test decides if an observation contains a multidimensional signal belonging to one subspace or if it contains a multidimensional signal belonging to an orthogonal subspace when unknown complex gaussian noise is present in our analysis we use a statistical hypothesis testing framework to develop a generalized likelihood ratio decision rule we evaluate the performance of this decision rule in both the matched and mismatched signal cases our results show that for constant power complex gaussian noise if the signal is matched to the steering vector abort glrt and amf give approximately equivalent probability of detection higher than that of ace which trades detection probability for an extra invariance to scale mismatch between training and test data of these four tests ace is most selective and therefore least tolerant of mismatch whereas amf is most tolerant of mismatch and therefore least selective abort and glrt offer compromises between these extremes with abort more like ace and with glrt more like amf

weyl product algebras and modulation spaces we discuss algebraic properties of the weyl product acting on modulation spaces for a certain class of weight functions omega we prove that m omega p q is an algebra under the weyl product if p epsilon 1 infinity and 1 q min p p for the remaining cases p epsilon 1 infinity and min p p q infinity we show that the unweighted spaces m p m q are not algebras under the weyl product c 2007 elsevier inc all rights reserved

adaptive detection of a subspace signal in signal dependent interference this paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal to this end at the design stage we assume that the signal dependent sd clutter shares the same subspace as the target signals as customary a set of secondary data free of signal components is also assumed available two adaptive detectors referred to as the sd rao and sd wald are proposed by resorting to the rao test and wald test design criteria unlike the classical rao and wald tests which are derived by dividing the complex parameter into the real and imaginary parts the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden moreover we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors

the analysis of golf swing as a kinematic chain using dual euler angle algorithm the manner in which anatomical rotation from an individual segment contributes to the position and velocity of the endpoint can be informative in the arena of many athletic events whose goals are to attain the maximal velocity of the most distal segment this study presents a new method of velocity analysis using dual euler angles and its application in studying rotational contribution from upper extremity segments to club head speed during a golf swing dual euler angle describes 3d movement as a series of ordered screw motions about each orthogonal axis in a streamlined matrix form the dual transformation matrix and allows the translation and rotation component to be described in the same moving frame applying this method in biomechanics is a novel idea and the authors have previously applied the methodology to clinical studies on its use in displacement analysis the focus of this paper is velocity analysis and applications in sports biomechanics in this study electrogoniometers biometrics uk with a frequency of 1000 hz were attached to a subject during the execution of the swing to obtain the joint angles throughout the motion the velocity of the club head was then analyzed using the dual velocity which specifies the velocity distribution of a rigid body in screw motion at any point in time as the dual vector the contributions of each segment to the club head velocity were also compared in order to evaluate this method the calculated position and velocity of the club head were compared to the values obtained from video image analysis the results indicated that there is good agreement between calculated values and video data suggesting the suitability of using the dual euler method in analyzing a kinematic chain motion

a unifying framework for adaptive radar detection in homogeneous plus structured interference part ii detectors design this paper deals with the problem of adaptive multidimensional multichannel signal detection in homogeneous gaussian disturbance with unknown covariance matrix and structured unknown deterministic interference the aforementioned problem extends the well known generalized multivariate analysis of variance gmanova tackled in the open literature in part i of this paper we have obtained the maximal invariant statistic mis for the problem under consideration as an enabling tool for the design of suitable detectors which possess the constant false alarm rate cfar property herein we focus on the development of several theoretically founded detectors for the problem under consideration first all the considered detectors are shown to be function of the mis thus proving their cfarness property second coincidence or statistical equivalence among some of them in such a general signal model is proved third strong connections to well known simpler scenarios analyzed in adaptive detection literature are established finally simulation results are provided for a comparison of the proposed receivers

inclusion relations between l p sobolev and wiener amalgam spaces abstract we determined optimal inclusion relations between l p sobolev and wiener amalgam spaces for applications we discuss mapping properties of unimodular fourier multipliers e i d between l p sobolev and wiener amalgam spaces and derive some littlewood paley type inequalities

the global cauchy problems for the nonlinear dispersive equations on modulation spaces abstract in this paper we discuss decay estimates and strichartz estimates for dispersive equations with non homogeneous symbols on modulation spaces m p q s to obtain the global well posedness of the cauchy problems for nonlinear dispersive equations as a result we have a generalization of the result in 19 which treated the schrodinger equations with a nonlinearity of wider class

invariant adaptive detection of range spread targets under structured noise covariance the invariance principle is adopted to develop an exhaustive study for adaptive detection of range spread targets in gaussian noise sharing a block diagonal covariance structure for this problem the usual generalized likelihood ratio principle is intractable in this paper we first determine the largest group of affine transformations that does not alter the decision problem then a maximal invariant identified by this group is derived which can characterize the totality of the invariant detectors and extends the existing results for the point target case a theoretical performance analysis of the maximal invariant is also given finally we propose two classes of invariant detectors which are distinguished by whether a constant false alarm rate cfar is maintained numerical experiments are provided for a comparison of the proposed detectors where a tradeoff between the cfarness and the improved performance has been observed and studied

globally well and ill posedness for non elliptic derivative schrodinger equations with small rough data abstract we show that there exists s c 0 such that the cubic quartic non elliptic derivative schrodinger equations with small data in modulation spaces m 2 1 s r n for n 3 n 2 are globally well posed if s s c and ill posed if s s c in 2d cubic case using the gabor frame we get some time global dispersive estimates for the schrodinger semi group in anisotropic lebesgue spaces which include a time global maximal function estimate in the space l x 1 2 l x 2 t by resorting to the smooth effect estimate together with the dispersive estimates in anisotropic lebesgue spaces we show that the cubic hyperbolic derivative nls in 2d has a unique global solution if the initial data in feichtinger segal algebra or in weighted sobolev spaces are sufficiently small

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

optimal invariant detection of a sinusoid with unknown parameters a uniformly most powerful test does not exist for the problem of detecting a sinusoid of unknown amplitude phase and frequency in complex white gaussian noise of unknown variance the problem is shown to be invariant to scale and modulation transformations using invariance principles it is found that the uniformly most powerful invariant umpi test does not exist a test is derived that is umpi if it is given that the signal to noise ratio snr is known for snr unknown the derived test can be used as an upper performance bound for any invariant test suboptimal tests are typically implemented such as the generalized likelihood ratio and locally most powerful tests which are also scale and modulation invariant it is shown analytically that as snr approaches zero the locally most powerful invariant test performance approaches the umpi performance bound and as the snr becomes large the generalized likelihood ratio test performance approaches the performance of the umpi bound computer simulation examples indicate that the generalized likelihood ratio test performance is close to the umpi bound particularly in the low probability of false alarm region of the receiver operating characteristic curve

cohen class of time frequency representations and operators boundedness and uncertainty principles abstract this paper presents a proof of an uncertainty principle of donoho stark type involving e concentration of localization operators more general operators associated with time frequency representations in the cohen class are then considered for these operators which include all usual quantizations we prove a boundedness result in the l p functional setting and a form of uncertainty principle analogous to that for localization operators

unimodular fourier multipliers on wiener amalgam spaces abstract we study the boundedness of unimodular fourier multipliers on wiener amalgam spaces for a real valued homogeneous function on r n of degree 2 we show the boundedness of the operator e i d between the weighted wiener amalgam space w s p q and w p q for all 1 p q and s n 2 1 p 1 2 n 1 p 1 q this threshold is shown to be optimal for regions max 1 q 1 2 1 p and min 1 q 1 2 1 p moreover we give sufficient conditions for the boundedness of e i d on w p q for 0 2

maximal invariants and performance of some invariant hypothesis tests for an adaptive detection problem maximal invariants for adaptive detection of a signal in unknown interference from multiple observations is derived given coherent samples from p sets of observations it is shown that a maximal invariant statistic for the detection problem is a 2p 1 dimensional vector comprising the eigenvalues of two hermitian positive definite matrices obtained from the data set two invariant detectors well known for p 1 are generalized for the case of multiple observations and closed form expressions for the probability of detection and probability of false alarm are derived along with the distributions of the signal to interference plus noise loss factors several novel invariant detectors are constructed from the maximal invariants and the receiver operating characteristics of the detectors compared

a characterization of modulation spaces by symplectic rotations abstract this note contains a new characterization of modulation spaces m m p r n 1 p by symplectic rotations precisely instead to measure the time frequency content of a function by using translations and modulations of a fixed window as building blocks we use translations and metaplectic operators corresponding to symplectic rotations technically this amounts to replace in the computation of the m m p r n norm the integral in the time frequency plane with an integral on r n u 2 n r with respect to a suitable measure u 2 n r being the group of symplectic rotations more conceptually we are considering a sort of polar coordinates in the time frequency plane to have invariance under symplectic rotations we choose a gaussian as suitable window function we also provide a similar and easier characterization with the group u 2 n r being reduced to the n dimensional torus t n

global wave front sets of banach frechet and modulation spacetypes and pseudo differential operators we introduce global wave front sets with respect to suitable banach or frechet spaces an important special case appears when choosing these spaces as modulation spaces we show that the standard p

performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments the adaptive sidelobe blanker asb algorithm is a two stage detector consisting of a first stage adaptive matched filter amf detector followed by a second stage detector called the adaptive coherence or cosine estimator ace only those data test cells that survive both detection thresholdings are declared signal target bearing we provide exact novel closed form expressions for the resulting probability of detection pd and false alarm pfa for the asb algorithm and demonstrate that under homogeneous data conditions with no signal array response mismatch that i the asb is a constant false alarm rate cfar algorithm ii the asb has a higher or commensurate pd for a given pfa than both the amf and the ace and iii the asb has an overall performance that is commensurate with kelly s 1986 benchmark generalized likelihood ratio test glrt a compact statistical summary is derived providing distributions and dependencies among the glrt amf and the ace decision statistics

glrt based direction detectors in homogeneous noise and subspace interference in this paper we derive and assess decision schemes to discriminate resorting to an array of sensors between the h0 hypothesis that data under test contain disturbance only i e noise plus interference and the h1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables the disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace we assume that a set of noise only secondary data is available which possess the same statistical characterization of noise in the cells under test at the design stage we resort to either the plain generalized likelihood ratio test glrt or the two step glrt based design procedure the performance analysis conducted resorting to simulated data shows that the one step glrt performs better than the detector relying on the two step design procedure when the number of secondary data is comparable to the number of sensors moreover it outperforms a one step glrt based subspace detector when the dimension of the signal subspace is sufficiently high

hormander multiplier theorem with regularity in modulation spaces abstract in this paper we mainly establish the hormander type multiplier theorem related to the modulation spaces m 2 p s r n for all 0 p 1 this extends the result of tomita 2009 when p 1 to all the cases 0 p 1 we use the littlewood paley stein square functions and atomic decompositions to establish our main result furthermore our method is substantially different from that used in tomita 2009 when p 1

pseudodifferential operators on modulation spaces abstract we establish a connection between certain classes of pseudodifferential operators and hille tamarkin operators as an application we find the conditions that guarantee compactness and summability of the eigenvalues of pseudodifferential operators acting on the modulation spaces m p p

time frequency analysis of the dirac equation abstract the purpose of this paper is to investigate several issues concerning the dirac equation from a time frequency analysis perspective more precisely we provide estimates in weighted modulation and wiener amalgam spaces for the solutions of the dirac equation with rough potentials we focus in particular on bounded perturbations arising as the weyl quantization of suitable time dependent symbols as well as on quadratic and sub quadratic non smooth functions hence generalizing the results in 40 we then prove local well posedness on the same function spaces for the nonlinear dirac equation with a general nonlinearity including power type terms and the thirring model for this study we adopt the unifying framework of vector valued time frequency analysis 56 most of the preliminary results are stated under general assumptions and hence they may be of independent interest

false alarm rate of the glrt for subspace signals in subspace interference plus gaussian noise in the presence of interference and gaussian noise with unknown covariance matrix a generalized likelihood ratio test glrt detector has already been developed for detecting a distributed target the target signal and interference are described with subspace models namely the target signals or interference are modeled as linear combinations of the linearly independent columns of a known subspace matrix in this paper we obtain statistical properties of this glrt detector and prove its constant false alarm rate against the noise covariance matrix moreover we derive analytical expressions for the probability of false alarm of the glrt detector specifically exact expressions for the probability of false alarm are obtained for six cases where the target subspace dimension denoted by p is 1 2 and 3 and the number of range cells denoted by h the distributed target occupies is 1 2 and 3 for the general case where p geq 4 and h geq 4 we derive an approximate expression for the probability of false alarm monte carlo simulations show that the exact expressions are valid and the accuracy of the approximate expression is acceptable for moderate or large training data size in practice these expressions can greatly facilitate the threshold setting for the glrt detector for any preassigned probability of false alarm

estimates on fractional power dissipative equations in function spaces abstract we study the fractional power dissipative equations whose fundamental semigroup is given by e t with 0 by using an argument of duality and interpolation we extend space time estimates of the fractional power dissipative equations in lebesgue spaces to the hardy spaces and the modulation spaces these results are substantial extensions of some known results as applications we study both local and global well posedness of the cauchy problem for the nonlinear fractional power dissipative equation u t u u m u for initial data in the modulation spaces

navier stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices abstract the cauchy problems for navier stokes equations and nonlinear heat equations are studied in modulation spaces m q s r n though the case of the derivative index s 0 has been treated in our previous work the case s 0 is also treated in this paper our aim is to reveal the conditions of s q and of m q s r n for the existence of local and global solutions for initial data u 0 m q s r n

continuity of magnetic weyl calculus abstract we investigate continuity properties of the operators obtained by the magnetic weyl calculus on nilpotent lie groups using modulation spaces associated with unitary representations of certain infinite dimensional lie groups

on the schatten von neumann properties of some pseudo differential operators abstract we obtain a number of explicit estimates for quasi norms of pseudo differential operators in the schatten von neumann classes s q with 0 q 1 the estimates are applied to derive semi classical bounds for operators with smooth or non smooth symbols

the dilation property of modulation spaces and their inclusion relation with besov spaces abstract we consider the dilation property of the modulation spaces m p q let d f t f t be the dilation operator and we consider the behavior of the operator norm d m p q m p q with respect to our result determines the best order for it and as an application we establish the optimality of the inclusion relation between the modulation spaces and besov spaces which was proved by toft j toft continuity properties for modulation spaces with applications to pseudo differential calculus i j funct anal 207 2004 399 429

performance of a class of adaptive detection algorithms in nonhomogeneous environments a two dimensional 2 d adaptive sidelobe blanker asb detection algorithm was developed through experimentation as an extenuate for false alarms caused by undernulled interference encountered when applying the adaptive matched filter amf in nonhomogeneous environments the algorithm s utility has been demonstrated empirically considering theoretic performance analyses of the asb detection algorithm as well as the amf generalized likelihood ratio test glrt and the adaptive cosine estimator ace under nonideal conditions can become fairly intractable rather quickly especially in an adaptive processing context involving covariance estimation in this paper however we have developed and exploited a theoretic framework through which the performance of these algorithms under nonhomogeneous conditions can be examined theoretically it is demonstrated through theoretic analysis that in the presence of undernulled interference the asb is a pliable false alarm regulatory far detector that maintains good target sensitivity a viable method of asb threshold selection is also presented and demonstrated

the inclusion relations between α modulation spaces and lp sobolev spaces or local hardy spaces abstract in this paper we first discuss equivalent norms for modulation spaces which are composed from decomposition with non compact frequency support then we determine sharp inclusion relations between modulation spaces and l p sobolev spaces and between modulation spaces and local hardy spaces

unimodular fourier multipliers for modulation spaces abstract we investigate the boundedness of unimodular fourier multipliers on modulation spaces surprisingly the multipliers with general symbol e i where 0 2 are bounded on all modulation spaces but in general fail to be bounded on the usual l p spaces as a consequence the phase space concentration of the solutions to the free schrodinger and wave equations are preserved as a byproduct we also obtain boundedness results on modulation spaces for singular multipliers sin for 0

the cauchy problem for the generalized zakharov kuznetsov equation on modulation spaces abstract we consider the cauchy problem for the generalized zakharov kuznetsov equation t u x 1 u x 1 u m 1 on three and higher dimensions we mainly study the local well posedness and the small data global well posedness in the modulation space m 2 1 0 r n for m 4 and n 3 we also investigate the quartic case i e m 3

schatten classes on compact manifolds kernel conditions abstract in this paper we give criteria on integral kernels ensuring that integral operators on compact manifolds belong to schatten classes a specific test for nuclearity is established as well as the corresponding trace formulae in the special case of compact lie groups kernel criteria in terms of locally and globally hypoelliptic operators are also given

closed loop problems in biomechanics part i a classification system biomechanics researchers have relied heavily on the inverse dynamics approach for calculating the forces and torques at human joints however implicit in this approach is the assumption that there are sufficient independent equations of motion to uniquely determine these unknown kinetics there exists a class of problems commonly referred to as closed loop problems when there are insufficient equations and indeterminacy arises the purposes of the present paper are 1 to develop a general classification system of closed loop problems for whole body movements and 2 to identify the minimum number of force transducing devices necessary to uniquely determine joint kinetics for these problems the classification system is based on the human subject s interaction with his environment and with himself two criteria are considered first the number of the subject s extremities in contact with fixed external reference systems and second the number of closed loops formed by those extremities not in contact with fixed external systems different combinations of these two criteria are examined and grouped into five cases according to the degree to which the equations of motion are over determined determined or under determined examples are given to illustrate the concepts it is felt that the use of this system should aid in the understanding of joint force and torque calculations especially with regard to the under determined cases

locally most powerful invariant tests for the properness of quaternion gaussian vectors previous works have addressed the second order statistical characterization of quaternion random vectors introducing different properness definitions and presenting the generalized likelihood ratio tests glrts for determining the kind of quaternion properness this paper considers the more challenging problem of deriving the locally most powerful invariant tests lmpits which can be obtained even without an explicit expression for the maximal invariants thanks to the wijsman s theorem specifically we consider three binary hypothesis testing problems involving the two main kinds of quaternion properness and show that the lmpit statistics are given by the frobenius norm of three previously defined sample coherence matrices the proposed detectors exhibit interesting connections with the problem of testing for the properness of a complex vector and with the problems of testing for the sphericity of a four dimensional real or two dimensional complex proper vector additionally some numerical examples show that in general the proposed lmpits outperform their glrt counterparts and in some cases the performance gap is very noticeable

adaptive detection of a signal known only to lie on a line in a known subspace when primary and secondary data are partially homogeneous this paper deals with the problem of detecting a signal known only to lie on a line in a subspace in the presence of unknown noise using multiple snapshots in the primary data to account for uncertainties about a signal s signature we assume that the steering vector belongs to a known linear subspace furthermore we consider the partially homogeneous case for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels this provides an extension to the framework considered by bose and steinhardt the natural invariances of the detection problem are studied which leads to the derivation of the maximal invariant then a detector is proposed that proceeds in two steps first assuming that the noise covariance matrix is known the generalized likelihood ratio test glrt is formulated then the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector the latter is compared with a similar detector that assumes the steering vector to be known

norm estimates for τ pseudodifferential operators in wiener amalgam and modulation spaces abstract we study continuity properties on modulation spaces for pseudodifferential operators op a with symbols a in wiener amalgam spaces we obtain boundedness results for 0 1 whereas in the end points 0 and 1 the corresponding operators are in general unbounded furthermore for 0 1 we exhibit a function of which is an upper bound for the operator norm the continuity properties of op a for any 0 1 with symbols a in modulation spaces are well known here we find an upper bound for the operator norm which does not depend on the parameter 0 1 as expected key ingredients are uniform continuity estimates for wigner distributions

stability of localized operators let lp 1 p be the space of all p summable sequences and ca be the convolution operator associated with a summable sequence a it is known that the lp stability of the convolution operator ca for different 1 p are equivalent to each other i e if ca has lp stability for some 1 p then ca has lq stability for all 1 q in the study of spline approximation wavelet analysis time frequency analysis and sampling there are many localized operators of non convolution type whose stability is one of the basic assumptions in this paper we consider the stability of those localized operators including infinite matrices in the sjostrand class synthesis operators with generating functions enveloped by shifts of a function in the wiener amalgam space and integral operators with kernels having certain regularity and decay at infinity we show that the lp stability or lp stability of those three classes of localized operators are equivalent to each other and we also prove that the left inverse of those localized operators are well localized

multilinear localization operators abstract in this paper we introduce a notion of multilinear localization operators by reinterpreting these operators as multilinear kohn nirenberg pseudodifferential operators we give sufficient conditions for their boundedness on products of modulation spaces moreover we prove that these conditions are also necessary for the boundedness of the operators finally as application we construct various examples of bounded multilinear pseudodifferential operators

strichartz estimates in the frame of modulation spaces abstract in this paper we study the strichartz estimates for three types of differential equations in the framework of modulation spaces the equations considered here include the wave equation the schrodinger equation and the nonelliptic schrodinger equation inhomogeneous equations of the above three types are also studied

the inclusion relation between sobolev and modulation spaces the inclusion relations between the lp sobolev spaces and the modulation spaces is determined explicitly as an application mapping properties of unimodular fourier multiplier ei d between lp sobolev spaces and modulation spaces are discussed

singular values of compact pseudodifferential operators abstract this paper investigates the asymptotic decay of the singular values of compact operators arising from the weyl correspondence the motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay the problem is approached by using a gabor frame expansion of the symbol to construct an approximating finite rank operator this establishes a variety of sufficient conditions for the associated operator to be in a particular schatten class in particular an improvement of a sufficient condition of daubechies for an operator to be trace class is obtained in addition a new development and improvement of the calderon vaillancourt theorem in the context of the weyl correspondence is given additional results of this type are then obtained by interpolation

frequency uniform decomposition method for the generalized bo kdv and nls equations abstract sufficient and necessary conditions for the embeddings between besov spaces b p q s 1 and modulation spaces m p q s 2 are obtained moreover using the frequency uniform decomposition method we study the cauchy problem for the generalized bo kdv and nls equations for which the global well posedness of solutions with the small rough data in certain modulation spaces m 2 1 s is shown

l2 estimates for weyl quantization abstract sharp l 2 estimates for weyl quantized pseudodifferential operators are established in the framework of hormander s classes of symbols s m in particular the case of forbidden symbols is discussed

gabor frames and time frequency analysis of distributions abstract this paper lays the foundation for a quantitative theory of gabor expansions f x k n c k n e 2 in x g x k in analogy to wavelet expansions of besov triebel lizorkin spaces we show that the correct class of spaces which can be characterized by the magnitude of the coefficients c k n is the class of modulation spaces to analyze the behavior of the coefficients it is necessary to invert the gabor frame operator on these spaces we show that the frame operator is invertible on modulation spaces if and only if it is invertible on l 2 and the atom g is in a suitable space of test functions a similar statement for wavelet theory is false the second part is devoted to gabor analysis on general time frequency lattices

functions operating on modulation spaces and nonlinear dispersive equations abstract the aim of this paper is two fold we show that if a complex function f on c operates in the modulation spaces m p 1 r n by composition then f is real analytic on r 2 c this answers negatively the open question posed in ruzhansky et al 2012 21 regarding the general power type nonlinearity of the form u u we also characterise the functions that operate in the modulation space m 1 1 r n the local well posedness of the nls nlw and nlkg equations for the real entire nonlinearities are also studied in some weighted modulation spaces m s p q r n

adaptive radar detection and localization of a point like target in the present paper we focus on the design of adaptive decision schemes for point like targets the proposed algorithms can take advantage of the possible spillover of target energy between consecutive matched filter samples to this end we assume that the received useful signal is known up to a complex factor modeled as a deterministic parameter moreover it is embedded in correlated gaussian noise with unknown covariance matrix finally for estimation purposes we assume that a set of secondary data free of signal components but sharing the same covariance matrix of the noise in the cells containing signal returns up to a possibly different scale factor is available remarkably the proposed decision schemes can provide accurate estimates of the target position within the cell under test and ensure the desirable constant false alarm rate property with respect to the unknown noise parameters

schatten classes for toeplitz operators with hilbert space windows on modulation spaces we prove that if 1 2 v 1 v 2 are appropriate j 1 2 and a in l p then the toeplitz operator tp h1 h2 a from m 2 omega 1 to m 2 omega 2 belongs to the schatten von neu

invariance theory for adaptive detection in interference with group symmetric covariance matrix this paper describes the adaptive detection of point like targets in a gaussian environment assuming a group symmetric structure for the interference covariance matrix this special configuration enforces block sparsity and permits splitting of the original observation space into lower dimensional subspaces each characterized by its own nuisance parameters hence the principle of invariance is invoked to select decision rules enjoying some symmetry defined by a suitable group of transformations which leave the decision problem unaltered all the invariant tests can be expressed as functions of a maximal invariant statistic whose derivation is among the key results of this paper finally some common design criteria are applied to come up with adaptive architectures that share invariance and their behavior is assessed to highlight the interplay between sample size and detection performance in comparison with conventional decision schemes

matched direction detectors and estimators for array processing with subspace steering vector uncertainties in this paper we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown in the presence of subspace interference and broad band noise this situation arises when on one hand there exist uncertainties about the steering vector but on the other hand some knowledge about the steering vector errors is available first we derive the maximum likelihood estimator mle for the problem and compute the corresponding crame spl acute r rao bound next the maximum likelihood estimates are used to derive a generalized likelihood ratio test glrt the glrt is compared and contrasted with the standard matched subspace detectors the performances of the estimators and detectors are illustrated by means of numerical simulations

the range of localization operators and lifting theorems for modulation and bargmann fock spaces we study the range of time frequency localization operators acting on modulation spaces and prove a lifting theorem as an application we also characterize the range of gabor multipliers and in t

characterization of inclusion relations between wiener amalgam and some classical spaces abstract in this paper we establish the sharp conditions for the inclusion relations between besov spaces b p q and wiener amalgam spaces w p q s we also obtain the optimal inclusion relations between local hardy spaces h p and wiener amalgam spaces w p q s which completely improve and extend the main results obtained by cunanana kobayashib and sugimotoa in 3 in addition we establish some mild characterizations of inclusion relations between triebel lizorkin and wiener amalgam spaces which relates some modern inequalities to classical inequalities

continuity properties for modulation spaces with applications to pseudo differential calculus i we discuss continuity for weighted modulation spaces andprove that many such spaces can be obtained in a canonicalway from the corresponding standard modulation spaces we also discussthe trace operator a a 0 acting on modulationspaces the results are used to get inclusions betweenmodulation spaces and besov spaces and proving continuityfor pseudo differential operators and toeplitz operators

a maximal invariant framework for adaptive detection with structured and unstructured covariance matrices we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing this involves calculating a low dimensional basis set of functions called the maximal invariant the statistics of which are often tractable to obtain thereby making analysis feasible and facilitating the search for tests with some optimality property using this approach we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published kelly s generalized likelihood ratio glrt and robey s adaptive matched filter amf test statistics applying this framework to structured covariance matrices corresponding to stochastic interferers in a known subspace for which the glrt is unavailable we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad hoc detectors these invariant tests are unaffected by most nuisance parameters hence the variation in the level of performance is sharply reduced this framework facilitates the search for such tests even when the usual glrt is unavailable

pseudodifferential operators on ultra modulation spaces abstract the boundedness of pseudodifferential operators on modulation spaces defined by the means of almost exponential weights is studied the results are applied to symbol class with almost exponential bounds including polynomial and ultra polynomial symbols the weyl correspondence is used and it is noted that the results can be transferred to the operators with appropriate anti wick symbols it is proved that a class of elliptic pseudodifferential operators can be almost diagonalized by the elements of wilson bases and estimates for their eigenvalues are given furthermore it is shown that the same can be done by using gabor frames

time frequency partitions and characterizations of modulation spaces with localization operators abstract we study families of time frequency localization operators and derive a new characterization of modulation spaces this characterization relates the size of the localization operators to the global time frequency distribution as a by product we obtain a new proof for the existence of multi window gabor frames and extend the structure theory of gabor frames

schatten von neumann properties in the weyl calculus let opt a for t r be the pseudo differential operator f x 2 n a 1 t x ty f y ei x y dyd and let ip be the set of schatten von neumann operators of order p 1 on l2 we are especially concerned with the weyl case i e when t 1 2 we prove that if m and g are appropriate metrics and weight functions respectively hg is the planck s function hgk 2m lp for some k 0 and a s m g then opt a ip iff a lp consequently if 0 1 and a s r then opt a is bounded on l2 iff a l

adaptive radar detection of a subspace signal embedded in subspace structured plus gaussian interference via invariance this paper deals with adaptive radar detection of a subspace signal competing with two sources of interference the former is gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise the latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna the problem is solved via the principle of invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant a maximal invariant statistic which completely characterizes the class of invariant decision rules and significantly compresses the original data domain as well as its statistical characterization are determined thus the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules at the analysis stage the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions

cfar detection of multidimensional signals an invariant approach the paper deals with constant false alarm rate cfar detection of multidimensional signals embedded in gaussian noise with unknown covariance we attack the problem by resorting to the principle of invariance which proves a valuable statistical tool for ensuring a priori namely at the design stage the cfar property in this context we determine a maximal invariant statistic with respect to a proper group of transformations that leave unaltered the hypothesis testing problem under study devise the optimum invariant detector and show that no uniformly most powerful invariant umpi test exists thus we establish the conditions an invariant detector must fulfill in order to ensure the cfar property finally we discuss several suboptimal implementable invariant receivers and remarkably show that the generalized likelihood ratio test glrt detector is a member of this class the performance analysis which has been carried out in the presence of a gaussian signal array shows that the proposed detectors exhibit a quite acceptable loss with respect to the optimum neyman pearson detector