uniform homeomorphisms of banach spaces and asymptotic structure we give a general result on the behavior of spreading models in banach spaces which coarse lipschitz embed into asymptotically uniformly convex spaces we use this result to study the uniqueness of the uniform structure in p sums of finite dimensional spaces for 1 p in particular we give some new examples of spaces with unique uniform structure

szlenk and w dentability indices of the banach spaces c 0 α abstract let be an infinite ordinal and the unique ordinal satisfying 1 we show that the banach space c 0 of all continuous scalar valued functions on the compact ordinal interval 0 has szlenk index equal to 1 and w dentability index equal to 1 1

on asymptotically uniformly smooth banach spaces abstract the class of asymptotically uniformly smoothable banach spaces has been considered in connection with several problems of nonlinear functional analysis as the differentiability of lipschitz functions the uniform classification of banach spaces or the fixed point property the known characterizations for those spaces come from p estimates when finite dimensional block decompositions are available or via duality by means of the szlenk index in this paper we found a geometrical characterization for the existence of asymptotically uniformly smooth renorming using an ordinal type index defined for subsets of the space among the applications we prove that the modulus of asymptotic uniform smoothness is the same for all the non asymptotically uniformly smoothable banach spaces

image restoration using the w slice method we propose the use of higher order statistics hos based methods to address the problem of image restoration the restoration strategy is based on the fact that the phase information of the original image and its hos are not distorted by some types of blurring the difficulties associated with the combination of 2 d signals and their hos are reduced by means of the radon transform two methods that apply the weight slice algorithm over the projections are developed simulation results illustrate the performance of the proposed methods

signal reconstruction from the phase of the bispectrum the authors present a simple procedure the bispectrum signal reconstruction bsr algorithm to recover the fourier phase of a signal from the phase of its bispectrum by simple analogy a procedure that recovers the fourier magnitude of a signal from the magnitude of its bispectrum is also presented in addition the authors propose an iterative scheme the bicepstrum iterative reconstruction algorithm bira for the reconstruction of a finite impulse response fir sequence from only the phase of its bispectrum and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the fourier phase of the signal whereas their sums contain the fourier magnitude information

finite slicing in superreflexive banach spaces abstract for every superreflexive banach space x there exists a supermultiplicative function which is the supremum in a very natural ordering of the set of all the moduli of convexity of equivalent norms if this supremum is actually a maximum achieved under some equivalent renorming of x then its modulus of convexity is the best possible in asymptotic sense otherwise we can give an almost optimal uniformly convex renorming of x beyond the classical power type bound obtained by pisier 21

ξ asymptotically uniformly smooth ξ asymptotically uniformly convex and β operators abstract for each ordinal we define the notions of asymptotically uniformly smooth and w asymptotically uniformly convex operators when 0 these extend the notions of asymptotically uniformly smooth and w asymptotically uniformly convex banach spaces we give a complete description of renorming results for these properties in terms of the szlenk index of the operator as well as a complete description of the duality between these two properties we also define the notion of an operator with property of rolewicz which extends the notion of property for a banach space we characterize those operators the domain and range of which can be renormed so that the operator has property in terms of the szlenk index of the operator and its adjoint

factorization of asplund operators abstract we give necessary and sufficient conditions for an operator a x y on a banach space having a shrinking fdd to factor through a banach space z such that the szlenk index of z is equal to the szlenk index of a we also prove that for every ordinal 0 1 1 a limit ordinal there exists a banach space g having a shrinking basis and szlenk index such that for any separable banach space x and any operator a x y having szlenk index less than a factors through a subspace and through a quotient of g and if x has a shrinking fdd a factors through g

structural characterization of locally optimum detectors in terms of locally optimum estimators and correlators explicit formulas for locally snr rightarrow 0 optimum mmse signal estimators smoother filter and predictor for discrete time observations of a random signal in additive random noise are derived and used to characterize the locally optimum likelihood ratio signal detector for on off signaling the characterizations are canonical distribution free detector structures involving estimator correlators these structural characterizations provide new interpretations of known detectors for various special cases if the one step signal predictor is recursive and the noise is white possibly non gaussian or nonstationary there is a canonical structure that admits recursive computation the primary motivation for these structural characterizations is to render the estimator correlator design philosophy applicable for the purpose of simplifying implementations and enhancing adaptability unlike the known esfimator correlator structural characterizations for continuous time globally optimum detectors the new characterizations apply for non gaussian as well as gaussian noise and the estimators are explicit rather than implicit

two channel likelihood detectors for arbitrary linear channel distortion this paper derives likelihood and generalized likelihood detection test statistics for a set of two channel problems this set includes additive gaussian and non gaussian noise known signals signals with unknown deterministic parameters signals with unknown statistical parameters and signals completely unknown the set also includes arbitrary linear channel distortion which is a generalization of time delay frequency shift and multipath simple expressions are obtained for the test statistic in the weak signal limit for additive non gaussian noise the ambiguity function is derived under the assumption of white gaussian noise with the signal completely unknown generalizations of the ambiguity function are derived and are used to construct detection statistics for other signal problems

three space property for asymptotically uniformly smooth renormings abstract we prove that if y is a closed subspace of a banach space x such that y and x y admit an equivalent asymptotically uniformly smooth norm then x also admits an equivalent asymptotically uniformly smooth norm the proof is based on the use of the szlenk index and yields a few other applications to renorming theory

algorithms for ambiguity function processing calculation of the complex ambiguity function is viewed as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise in many applications the required accuracy leads to a need for integration over long data sets that can become a challenge for near real time digital processing the nature of the ambiguity processing is interpreted and an algorithm approach is shown that minimizes the processing burden over a broad category of applications without affecting performance

detection and source location of weak cyclostationary signals simplifications of the maximum likelihood receiver the problem of dual receiver interception of low snr signals which includes detection of the presence of a particular signal type and location of its source is considered in particular source location based on time difference of arrival tdoa measurements is examined and the low snr maximum likelihood receiver for joint detection and tdoa estimation is taken as a starting point by explicitly revealing the way in which this receiver exploits the spectral correlation properties of the cyclostationary signal several partial implementations with optimality properties of their own are proposed these greatly simplified implementations which require only a one dimensional search over the tdoa parameter are shown by simulation to perform competitively with the relatively complicated maximum likelihood receiver which requires a two or three dimensional search for phase shift keyed psk signals

operators on c k spaces preserving copies of schreier spaces it is proved that an operator t c k x k compact metrizable x a separable banach space for which the e szlenk index of t bx is greater than or equal to 1 is an isomorphism on a subspace of c k isomorphic to x the schreier space of order as a corollary one obtains that a complemented subspace of c k with szlenk index equal to 1 contains a subspace isomorphic to x

k β and k nearly uniformly convex banach spaces vol 162 no 2 1991 k and k nearly uniformly convex banach spaces denka kutzarova different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of banach spaces in the present paper we introduce other properties of this type namely k and k nearly uniform convexity the definitions as well as some of the results presented here are announced in 7 sullivan 24 has defined k uniformly rotund banach spaces which by a suggestion of davis are all superreflexive fan and glicksberg 1 have introduced fully k convex banach spaces let x1 xk 1 be vectors in a banach space x the k dimensional volume enclosed by x1 xk 1 is given by v x1 x2 xk 1

the uniform structure of banach spaces we explore the existence of uniformly continuous sections for quotient maps using this approach we are able to give a number of new examples in the theory of the uniform structure of banach spaces we show for example that there are two non isomorphic separable mathcal l 1 subspaces of l1 which are uniformly homeomorphic we also prove the existence of two coarsely homeomorphic banach spaces i e with lipschitz isomorphic nets which are not uniformly homeomorphic answering a question of johnson lindenstrauss and schechtman we construct a closed subspace of l1 whose unit ball is not an absolute uniform retract answering a question of the author

direct sums and the szlenk index abstract for an ordinal and 1 p we determine a necessary and sufficient condition for an l p direct sum of operators to have szlenk index not exceeding it follows from our results that the szlenk index of an l p direct sum of operators is determined in a natural way by the behaviour of the e szlenk indices of its summands our methods give similar results for c 0 direct sums

system identification using a linear combination of cumulant slices a linear approach to identifying the parameters of a moving average ma model from the statistics of the output is presented first it is shown that under some constraints the impulse response of the system can be expressed as a linear combination of cumulant slices then this result is used to obtain a well conditioned linear method for estimating the ma parameters of a nongaussian process the linear combination of slices used to compute the ma parameters can be constructed from different sets of cumulants of different orders provided a general framework in which all the statistics can be combined it is not necessary to use second order statistics autocorrelation slice and therefore the proposed algorithm still provides consistent estimates in the presence of colored gaussian noise another advantage of the method is that while most linear methods give totally erroneous estimates if the order is overestimated the proposed approach does not require a previous estimation of the filter order the simulation results confirm the good numerical conditioning of the algorithm and its improvement in performance in comparison to existing methods

the szlenk index of injective tensor products and convex hulls abstract given any banach space x and any weak compact subset k of x we compute the szlenk index of the weak closed convex hull of k as a function of the szlenk index of k also as an application we compute the szlenk index of any injective tensor product of two operators in particular we compute the szlenk index of an injective tensor product x e y in terms of s z x and s z y as another application we give a complete characterization of those ordinals which occur as the szlenk index of a banach space as well as those ordinals which occur as the bourgain l 1 or c 0 index of a banach space

detection of weak signals in non gaussian noise a locally optimum detector structure is derived for the detection of weak signals in non gaussian environments optimum performance is obtained by employing a zero memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise gaussian the asymptotic detection performance of the locally optimum detector under non gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in gaussian noise numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest

power type ξ asymptotically uniformly smooth and ξ asymptotically uniformly flat norms abstract for each ordinal and each 1 p we offer a natural isomorphic characterization of those spaces and operators which admit an equivalent p asymptotically uniformly smooth norm we also introduce the notion of asymptotically uniformly flat norms and provide an isomorphic characterization of those spaces and operators which admit an equivalent asymptotically uniformly flat norm given a compact hausdorff space k we prove an optimal renorming theorem regarding the asymptotic smoothness of c k in terms of the cantor bendixson index of k we also prove that for all ordinals both the isomorphic properties and isometric properties pass from banach spaces to their injective tensor products we study the classes of p asymptotically uniformly smooth p asymptotically uniformly smoothable asymptotically uniformly flat and asymptotically uniformly flattenable operators we show that these classes are either a banach ideal or a right banach ideal when assigned an appropriate ideal norm

classes of operators determined by ordinal indices abstract we introduce and study the bourgain index of an operator between two banach spaces in particular we study the bourgain l p and c 0 indices of an operator several estimates for finite and infinite direct sums are established we define classes determined by these indices and show that some of these classes form operator ideals we characterize the ordinals which occur as the index of an operator and establish exactly when the defined classes are closed we study associated indices for non preservation of l p and c 0 spreading models and indices characterizing weak compactness of operators between separable banach spaces we also show that some of these classes are operator ideals and discuss closedness and distinctness of these classes

embedding uniformly convex spaces into spaces with very few operators we prove that every separable uniformly convex banach space x embeds into a banach space z which has the property that all bounded linear operators on z are compact perturbations of scalar multiples of the identity more generally the result holds for all separable reflexive banach spaces of szlenk index 0

direct sums and summability of the szlenk index abstract we prove that the c 0 sum of separable banach spaces with uniformly summable szlenk index has summable szlenk index whereas this result is no longer valid for more general direct sums we also give a formula for the szlenk power type of the e direct sum of separable spaces provided that e has a shrinking unconditional basis whose dual basis yields an asymptotic l p structure in e as a corollary we show that the tsirelson direct sum of infinitely many copies of c 0 has power type 1 but non summable szlenk index

twisted sums with c k spaces if x is a separable banach space we consider the existence of non trivial twisted sums 0 c k y x 0 where k 0 1 or for the case k 0 1 we show that there exists a twisted sum whose quotient map is strictly singular if and only if x contains no copy of 1 if k we prove an analogue of a theorem of johnson and zippin for k 0 1 by showing that all such twisted sums are trivial if x is the dual of a space with summable szlenk index e g x could be tsirelson s space a converse is established under the assumption that x has an unconditional finite dimensional decomposition we also give conditions for the existence of a twisted sum with c with strictly singular quotient map

szlenk indices of convex hulls we study the general measures of non compactness defined on subsets of a dual banach space their associated derivations and their iterates we introduce the notions of convexifiable and sublinear measure of non compactness and investigate the properties of its associated fragment and slice derivations we apply our results to the kuratowski measure of non compactness and to the study of the szlenk index of a banach space as a consequence we obtain that the szlenk index and the convex szlenk index of a separable banach space are always equal we also give for any countable ordinal a characterization of the banach spaces with szlenk index bounded by 1 in terms of the existence of an equivalent renorming this extends a result by knaust odell and schlumprecht on banach spaces with szlenk index equal to

weak dentability index of spaces c 0 α abstract we compute the weak dentability index of the spaces c k where k is a countable compact space namely dz c 0 1 1 whenever 0 1 more generally dz c k 1 1 if k is a scattered compact whose height k satisfies k 1 with an countable

dentability indices with respect to measures of non compactness abstract we study the relationships between the ordinal indices of set derivations associated to several measures of non compactness we obtain applications to the szlenk index improving a result of lancien and lur renorming providing a non probabilistic proof of a result of troyanski

on zippin s embedding theorem of banach spaces into banach spaces with bases abstract we present a new proof of zippin s embedding theorem that every separable reflexive banach space embeds into one with shrinking and boundedly complete basis and every banach space with a separable dual embeds into one with a shrinking basis this new proof leads to improved versions of other embedding results

the universality of l1 as a dual space let x be a banach space with a separable dual we prove that x embeds isomorphically into a mathcal l infty space z whose dual is isomorphic to l1 if moreover u is a space with separable dual so that u and x are totally incomparable then we construct such a z so that z and u are totally incomparable if x is separable and reflexive we show that z can be made to be somewhat reflexive

proximity to l1and distortion in asymptotic l1spaces abstract for an asymptotic l 1 space x with a basis x i certain asymptotic l 1 constants x are defined for 1 x measures the equivalence between all normalized block bases y i k i 1 of x i which are s admissible with respect to x i s is the th schreier class of sets and the unit vector basis of l k 1 this leads to the concept of the delta spectrum of x x which reflects the behavior of stabilized limits of x the analogues of these constants under all renormings of x are also defined and studied we investigate x both in general and for spaces of bounded distortion we also prove several results on distorting the classical tsirelson s space t and its relatives

proximity to lp and c0 in banach spaces abstract we construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees among the applications of these trees and coloring theorems are quantification of the bourgain l p and c 0 indices dualization of the bourgain c 0 index establishing sharp positive and negative results for constant reduction and estimating the bourgain l p index of an arbitrary banach space x in terms of a subspace y and the quotient x y

backprojection by upsampled fourier series expansion and interpolated fft a fast backprojection method through the use of interpolated fast fourier transform fft is presented the computerized tomography ct reconstruction by the convolution backprojection cbp method has produced precise images however the backprojection part of the conventional cbp method is not very efficient the authors propose an alternative approach to interpolating and backprojecting the convolved projections onto the image frame first the upsampled fourier series expansion of the convolved projection is calculated then using a gaussian function it is projected by the aliasing free interpolation of fft bins onto a rectangular grid in the frequency domain the total amount of computation in this procedure for a 512 512 image is 1 5 of the conventional backprojection method with linear interpolation this technique also allows the arbitrary control of the frequency characteristics

szlenk indices and uniform homeomorphisms we prove some rather precise renorming theorems for banach spaces with szlenk index wo we use these theorems to show the invariance of certain quantitative szlenk type indices under uniform homeomorphisms

compact spaces of szlenk index ω abstract the szlenk index has found many applications in the isomorphic theory of banach spaces its definition is based in some kind of interplay between a weak topology and the norm metric with not much care on the linear structure there is no obstacle to consider the notion of szlenk index in more general settings in this paper we study the compact spaces of szlenk index at most with respect to an associated metric we include new applications to banach spaces of the these methods where the estimations of the growth speed of the finite szlenk indices play a fundamental role

the coarse lipschitz geometry of ell_p oplus ell_q we show that for 1 p with p 2 the space l p 0 1 is not uniformly homeomorphic to ell p oplus ell 2 we also show that if 1 p 2 q the space ell p oplus ell q has unique uniform structure answering a question of johnson lindenstrauss and schechtman geom funct anal 6 430 470 1996

non three space properties and szlenk index abstract we prove that for any non zero countable ordinal which is not additively indecomposable the property of having szlenk index not exceeding is not a three space property this complements a result of brooker and lancien which states that if is additively indecomposable then having szlenk index not exceeding is a three space property

super wcg banach spaces abstract a banach space x admits an equivalent strongly uniformly g teaux smooth norm if and only if it contains the dense range of a super weakly compact operator which is equivalent to say that x is generated by a convex super weakly compact set moreover if x is strongly generated by a convex super weakly compact set then there is an equivalent norm on x such that its restriction to any reflexive subspace of x is both uniformly convex and uniformly frechet smooth