the yang mills equations on the universal cosmos global existence and regularity of solutions for the yang mills equations on the universal cosmos m which has the form r1 s3 for each of an 8 parameter continuum of factorizations of m as time space are treated by general methods the cauchy problem in the temporal gauge is globally soluble in its abstract evolutionary form with arbitrary data for the field potential in l2 r s3 l2 r 1 s3 where r is an integer 1 and l2 r denotes the class of sections whose first r derivatives are square integrable if r 1 the problem is soluble locally in time when r is 3 or more the solution is identifiable with a classical one if infinite the solution is in c m these results extend earlier work and approaches 1 5 solutions of the equations on minkowski space time m0 extend canonically modulo gauge transformations to solutions on m provided their cauchy data are moderately smooth and small near spatial infinity precise asymptotic structures for solutions on m0 follow and in turn imply various decay estimates thus the energy in regions uniformly bounded in direction away from the light cone is o x0 5 where x0 is the minkowski time coordinate analysis solely in m0 8 9 earlier yielded the estimate o x0 2 applicable to the region within the light cone similarly it follows that the action integral for a solution of the yang mills equations in m0 is finite in fact absolutely convergent

analysis in space time bundles iii higher spin bundles the universal cosmos m is the unique four dimensional globally causal space time manifold to which the dirac and maxwell equations among others maximally and covariantly extend a systematic treatment is presented of general fields over m of arbitrary spin considered are fields induced from all irreducible representation of the isotropy group scale extended poincare group to g the connected causal group of m restricted to any species of such fields the k invariant canonical dirac operator k maximal essentially compact subgroup of g is shown g covariant for a unique conformal weight a normalized k finite basis for such fields is constructed the basis actions thereon of the dirac operator infinitesimal generators of g discrete symmetries second order casimir and the essentially unique third order noncentral quantum number enveloping algebra element invariant under k are derived composition series under g of a class of these field spaces namely the extension to m of the relativistic fields considered by bargman and wigner or arbitrary spin and conformal weight are determined distinguishing by invariance and causality features alone the essentially conventional positive energy mass 0 subspaces and massive invariant sub quotient spaces whose unitarity under g is given a new proof the completely positive subclass cf below of representations is determined a more detailed treatment of spin one bundles vector and two form of arbitrary conformal weight is included the exterior derivative transformations are diagonalized and the conformally invariant massive spin one scalar product is identified with a mathematical version of the conventional electromagnetic field lagrangian

nonlinear quantum fields in 4 dimensions and cohomology of the infinite heisenberg group aspects of the cohomology of the infinite dimensional heisenberg group as represented on the free boson field over a given hilbert space are treated the 1 cohomology is shown to be trivial in certain spaces of generalized vectors from this derives a canonical quantization mapping from classical unquantized forms to generalized operators on the boson field an example applied here to scalar relativistic fields is the quantization of a given classical interaction lagrangian or hamiltonian i e the establishment and characterization of corresponding boson field operators for example if q denotes the free massless scalar field in d dimensional minkowski space d 4 even and if q is an even integer greater than or equal to 4 then f smo x q dx exists as a nonvanishing poincare invariant hermitian selfadjointly extendable operator where o x q denotes the wick power applications are also made to the rigorous establishment of basic symbolic operators in heuristic quantum field theory including certain massive field theories to a class of pseudo interacting fields obtained by substituting the free field into desingularized expressions for the total hamiltonian in the conformally invariant case d q 4 and to corresponding scattering theory

identification of time varying systems in reproducing kernel hilbert spaces we consider a class of linear systems in state space form whose parameters evolve in time according to a continuous time gauss markov process our problem is to identify the system from a finite set of noisy output measurements we derive a connection between this problem and tikhonov regularization in reproducing kernel hilbert spaces relying upon this result conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out simulated data are used to test the goodness of the proposed approach

scattering for the yang mills equations we construct wave and scattering operators for the yang mills equations on minkowski space m 0 r 4 sufficiently regular solutions of the yang mills equations on m 0 are known to extend uniquely to solutions of the corresponding equations on the universal cover of its conformal compactification m rxs 3

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

on an example of a complex symmetric composition operator on h2 d abstract in the article 8 an example of a composition operator c on the hardy space h 2 d is discovered that is claimed to be complex symmetric but not normal the purpose of this note is to highlight a mistake in the example that makes the result incorrect

conformally invariant differential equations and projective geometry abstract we combine harmonic analysis on certain pseudo riemannian symmetric spaces with results on conformally invariant linear and non linear differential equations this gives in many cases part of the decomposition of certain representations of the conformal group of a manifold when restricted to the isometry group

approximation numbers of composition operators on h p spaces of dirichlet series by a theorem of gordon and hedenmalm generates a bounded composition operator on the hilbert space h2 of dirichlet series nbnn s with square summable coefficients bn if and only if s c0s s where c0 is a nonnegative integer and a dirichlet series with the following mapping properties maps the right half plane into the half plane res 1 2 if c0 0 and is either identically zero or maps the right half plane into itself if c0 is positive it is shown that the nth approximation numbers of bounded composition operators on h2 are bounded below by a constant times rn for some 0 0 when c0 is positive both results are best possible the case when c0 0 is bounded and smooth up to the boundary of the right half plane and sup re 1 2 is discussed in depth it includes examples of non compact operators as well as operators belonging to all schatten classes sp for s c1 j 1dcqjqj s with qj independent integers it is shown that the nth approximation number behaves as n d 1 2 possibly up to a factor log n d 1 2 estimates rely mainly on a general hilbert space method involving finite linear combinations of reproducing kernels a key role is played by a recently developed interpolation method for h2 using estimates of solutions of the equation finally by a transference principle from h2 of the unit disc explicit examples of compact composition operators with approximation numbers decaying at essentially any sub exponential rate can be displayed

spectrum estimation of short time stationary signals in additive noise and channel distortion in this work spectrum estimation of a short time stationary signal that is degraded by both channel distortion and additive noise is addressed a maximum likelihood estimation mle algorithm is developed to jointly identify the degradation system and estimate short time signal spectra the source signal is assumed to be generated by a hidden markov model hmm with state dependent short time spectral distributions described by mixtures of gaussian densities the distortion channel is linear time invariant and the noise is gaussian the algorithm is derived by using the principle of expectation maximization em where the unknown parameters of channel and noise are estimated iteratively and the short time signal power spectra are obtained from the posterior sufficient statistics of the source signal other spectral representation parameters such as autoregressive model parameters or cepstral parameters are obtained by minimum mean squared error mmse estimation from the power spectral estimates the estimation algorithm was evaluated on simulated signals at the signal to noise ratios snrs of 20 db down to 0 db where it produced convergent estimation and significantly reduced spectral distortion

optimal joint detection estimation in fading channels with polynomial complexity the problem of sequence detection in frequency nonselective time selective fading channels when channel state information csi is not available at the transmitter and receiver is considered in this paper the traditional belief is that exact maximum likelihood sequence detection mlsd of an uncoded sequence over this channel has exponential complexity in the channel coherence time thus for slowly varying channels i e channels having coherence time on the order of the sequence length the complexity appears to be exponential in the sequence length in the first part of this work it is shown that exact mlsd can be computed with only polynomial worst case complexity in the sequence length regardless of the operating signal to noise ratio snr for equal energy signal constellations by establishing a relationship between the aforementioned complexity and the rank of the correlation matrix of the fading process an understanding of how complexity of the optimal mlsd receiver varies as the channel dynamics change is provided in the second part of this paper the problem of decoding turbo like codes in frequency nonselective time selective fading channels without receiver csi is examined using arguments similar to the ones used for the mlsd case it is shown that the exact symbol by symbol soft decision metrics sbssdms implied by the min sum algorithm can be evaluated with polynomial worst case complexity in the sequence length regardless of snr for equal energy signal constellations finally by simplifying some key steps in the polynomial complexity algorithm a family of fast approximate algorithms is derived which yield near optimal performance

analysis in space time bundles iv natural bundles deforming into and composed of the same invariant factors as the spin and form bundles abstract we study two interesting new bundles over the universal cosmos m or maximal isotropic space time which may be physically applicable the treatment is from a homogeneous vector bundle point of view and uses the notation and some of the results of the treatment in papers i iii s m paneitz and i e segal j funct anal 47 1982 78 142 49 1982 335 414 54 1983 18 22 of conventional bundles over m the spannor bundle deforms into essentially the usual spinor bundle as a conformally invariant parameter that may be interpreted as the space curvature becomes arbitrarily small from a minkowski space standpoint however the spannors involve a nontrivial action of space time translations that deforms into a trivial action in the spinor limit and also have more complex transformation properties under discrete symmetries also studied are the plyors consisting of the dual to the bundle product of the spannors with themselves composition series for the spannor and plyor section spaces are treated relative to the conformal group and irreducible subquotients are identified with certain that occur in conventional bundles in particular factors corresponding to the maxwell and massless dirac equations and which may represent certain of the observed elementary particles are determined a gauge and conformally invariant nonlinear coupling between spannors and plyors constituting essentially a generalization of that used in quantum electrodynamics is developed and an associated invariant nonlinear partial differential equation is derived covariant and causal quantization for spannors as fermions and plyors as bosons is formulated algebraically the present treatment is basically mathematical but physical motivations and possible interpretations are briefly noted

composition operators on weighted bergman spaces of dirichlet series abstract we study boundedness and compactness of composition operators on weighted bergman spaces of dirichlet series particularly we obtain in some specific cases upper and lower bounds of the essential norm of these operators and a criterion of compactness on classical weighted bergman spaces moreover a sufficient condition of compactness is obtained using the notion of carleson s measure

semi blind simo flat fading channel estimation in unknown spatially correlated noise using the em algorithm we present a maximum likelihood ml method for semi blind estimation of single input multi output simo flat fading channels in spatially correlated noise having unknown covariance an expectation maximization em algorithm is utilized to compute the ml estimates of the channel and spatial noise covariance we derive the crame spl acute r rao bound crb matrix for the unknown parameters and present a symbol detector that utilizes the em channel estimates numerical simulations demonstrate the performance of the proposed method

sequence estimation and synchronization from nonsynchronized samples the authors study the problem of maximum likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate which is assumed perfectly known by the receiver a general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates it is observed that the optimal processing of the matched filter samples consists of digital interpolation followed by symbol by symbol decoding when sampling is at or above the nyquist rate or viterbi decoding when sampling is below the nyquist rate performance is studied through the cramer rao bound on mean square estimation error and a lower bound on error probability

iterative symbol timing recovery for short burst transmission schemes this paper presents a novel iterative symbol timing recovery str scheme for short burst transmission formats a paradigm commonly found in modern wireless systems like for instance time division multiple access tdma schemes and future wireless packet data networks both data aided da and decision directed dd solutions are considered and performance is pursued by means of an iterative burst by burst scheme which exploits the farrow structure for the polynomial interpolation filter the convergence of the algorithm is discussed according to the expectation maximization em framework performance is evaluated by simulating 4 qam and 16 qam transceivers and simulations results are compared under different modulation orders and channel conditions for both the decision directed and data aided cases

a multiuser receiver for code division multiple access communications over multipath channels a multiuser communication system is considered where k users share a channel with multipath propagation by using code division for multiple access data modulation is carried out by binary phase shift keying and direct sequence spread spectrum signaling the micro cellular communication media is modeled as a frequency selective fading channel with multipath propagation the multipath diversity of the received signals from the k users is exploited by a bank of k rake correlators algorithms based on the maximum likelihood rule have been developed for estimating the complex channel coefficients as well as for detection of the desired data packets from the sufficient statistics provided by the rake correlators the performance of the resulting multiuser detector is evaluated analytically and via monte carlo simulations the results indicate that the estimator of the channel coefficients has a variance close to the cramer rao lower bound and that the proposed multiuser detector is capable of eliminating the near far effect as well as processing the signals propagated through multiple paths

scattering and the geometry of the solution manifold of ƒ λƒ3 0 abstract the wave transforms for the equation 3 0 on r 4 can be represented as maps from the hilbert space h s of finite energy cauchy data for the equation 1 3 0 on r 4 s 3 to hilbert spaces h c of finite energy goursat data we show that the wave transforms and associated scattering transform are diffeomorphisms the action of the group g so 2 4 on solutions of the latter equation gives rise to actions of g as diffeomorphisms of h s and h c which are intertwined by the wave and scattering transforms moreover the spaces h s and h c have symplectic structures relative to which the group g and the wave and scattering transforms act as symplectomorphisms these symplectic structures extend to flat kahler structures that are invariant under the scaling extended poincare group p

spinor currents as vector particles abstract we study a prototype for the problem of determining the irreducible factors of the spaces spanned by currents between homogeneous vector bundles more specifically let g denote the conformal group of minkowski space time m 0 or more precisely su 2 2 it is shown that the positive energy unitary g irreducible massive factors of the one form bundle over the conformal compactification of m 0 are bundle equivalent to spaces spanned by currents of the spinor bundle this has the interpretation that the z particle may be modelled by the representation of g of lowest k type lkt 3 emsp14 1 2 1 2 where k su 1 su 2 su 2 and m j j refers to the representation in which the lowest eigenvalue of the su 1 generator is m while j and j are the spins of the left and right su 2 representations in particular this z representation is bundle equivalent to the representation of g in a space of currents between neutrinos of lkt 3 2 0 1 2 and antineutrinos of lkt 3 2 1 2 0 the w particle representation may similarly be modelled by the representation of g of lowest k type 4 0 0 the only other massive positive energy unitary factor of the one form bundle in particular the w is equivalent to a space of currents between the electron of lkt 5 2 0 1 2 and the antineutrino these results are consistent with the possibility that all quasi stable elementary particles may be modelled by similar subspaces of bundle products

conditional moment generating functions for integrals and stochastic integrals in this paper we present two methods for computing filtered estimates for moments of integrals and stochastic integrals of continuous time nonlinear systems the first method utilizes recursive stochastic partial differential equations the second method utilizes conditional moment generating functions an application of these methods leads to the discovery of new classes of finite dimensional filters for the case of gaussian systems the recursive computations involve integrations with respect to gaussian densities while the moment generating functions involve differentiations of parameter dependent ordinary stochastic differential equations these filters can be used in volterra or wiener chaos expansions and the expectation maximization algorithm the latter yields maximum likelihood estimates for identifying parameters in state space models

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

harmonic analysis on spannors the spannor representation of the universal covering group of the conformal group of minkowski space time is studied herein it is an example of an indecomposable representation various parallelizations for spannors are described normalized k finite basis fields for the spannors are introduced and a computation of the actions of the scale generator and other generators of the conformal group on these basis fields is given the irreducibility of all irreducible composition factors is established and it is decided which ones are infinitesimally unitary two sets of generators for maximal abelian subalgebras of the enveloping algebra of the conformal group are introduced the action of one of the sets on k finite basis fields in the spannor representation is studied this is important for understanding of the problem of degeneracy in the spannor representation since k types occur with multiplicity 2 many calculations make use of the lowest highest weight module structures of the unitarizable and positive negative energy irreducible composition factors and thus many of our results and techniques can be used to initiate a study of the quantum deformations of the associated lie algebra representations results on the poincare content of the unitarizable irreducible composition factors are stated and unitary equivalences between certain of these factors are established

joint parameter estimation and symbol detection for linear or nonlinear unknown channels we present an iterative method for joint channel parameter estimation and symbol selection via the baum welch algorithm or equivalently the expectation maximization em algorithm channel parameters including noise variance are estimated using a maximum likelihood criterion the markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward backward algorithm the calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability the proposed receiver can be used for both linear and nonlinear channels it improves the system throughput by making saving in the transmission of known symbols usually employed for channel identification simulation results which show fast convergence are presented

the baum welch algorithm for the detection of time unsynchronized rectangular pam signals the theory of hidden markov models is used to formulate an iterative method for the joint estimation of timing phase offset and the detection of symbols carried by a time unsynchronized pam signal block timing phase offset estimation is based on the maximum likelihood criterion posterior probabilities of symbols are calculated and used to perform symbol by symbol decisions minimizing the symbol error probability

application of expectation maximization algorithm to the detection of a direct sequence signal in pulsed noise jamming the detection of a direct sequence spread spectrum signal received in a pulsed noise jamming environment is considered the expectation maximization algorithm is used to estimate the unknown jammer parameters and hence obtain a decision on the binary signal based on the estimated likelihood functions the probability of error performance of the algorithm is simulated for a repeat code and a 7 4 block code simulation results show that at low signal to thermal noise ratio and high jammer power the em detector performs significantly better than the hard limiter and somewhat better than the soft limiter also at low snr there is little degradation as compared to the maximum likelihood detector with true jammer parameters at high snr the soft limiter outperforms the em detector

parametrization of causal actions of universal covering groups and global hyperbolicity abstract the transformation group of the universal covering of the real projective line obtained by lifting ordinary projective transformations is given explicitly in terms of canonical coordinates a similar formulation is given of the action of the universal covering of su 2 2 upon the universal covering of the shilov boundary of its associated bounded hermitian symmetric domain structured as r1 su 2 the former group g isomorphic to s u 1 1 has a unique and continuous bi invariant global partial ordering similar to that expressing space time causality relations corresponding to its bivariant lorentzian metric the partial ordering is the same as that induced by the ordering of the real line which the transformation group preserves as an application the compactness of the intervals g 1 g 2 g g g 1 g g 2 for g 1 g 2 g necessary for global hyperbolicity of the metric is studied it is shown that g1 g2 is compact if and only if g g1 for all g in a neighborhood of g2 where is the generator of the center of g satisfying e in particular the interior of e is a maximal open global hyperbolic submanifold s u 1 1 is not globally hyperbolic

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

complex symmetric composition operators on h2 abstract in this paper we find complex symmetric composition operators on the classical hardy space h 2 whose symbols are linear fractional but not automorphic in doing so we answer a recent question of noor and partially answer the original problem posed by garcia and hammond

elementary representations and intertwining operators for su 2 2 i the structure of the group su 2 2 and of its lie algebra is studied in detail the results will be applied in subsequent parts devoted to the explicit construction of elementary representations of su 2 2 induced from different parabolic subgroups and of the intertwining operators between these representations a summary of some results of parts ii and iii is given

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

complex symmetric weighted composition operators on h2 d abstract in this paper we study complex symmetric weighted composition operators on the hardy space we provide some characterizations of and when a weighted composition operator w is complex symmetric we investigate which combinations of weights and maps of the open unit disk give rise to complex symmetric weighted composition operators with a special conjugation as some applications we obtain several examples for nonnormal complex symmetric operators in addition we give spectral properties of complex symmetric weighted composition operators we examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is hilbert schmidt finally we consider cyclicity hypercyclicity and the single valued extension property for complex symmetric weighted composition operators

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

compactness of composition operators on a hilbert space of dirichlet series abstract in this paper new l p l q estimates are proved for translation invariant radon transforms along curves for and p q for a fixed and if p is sufficiently close to 2 the best possible q is obtained up to e the method is related to that of 5

analysis in space time bundles i general considerations and the scalar bundle abstract mathematical features involved in the systematic development of elementary particle theory on an alternative cosmos space time are presented bundles representative of physical fields are studied in the unique variant of minkowski space m 0 enjoying similar properties of causality and symmetry the universal cosmos m is the universal cover of the causal compactification of m 0 the bundles studied are induced from representations of the scale extended poincare group which forms the isotropy group in m of the universal cover g s u 2 2 of the connected component of the group of all causal transformations on m discrete symmetries and higher dimensional cases are also discussed the primary focus is on the temporal evolution especially stability involving positivity of the energy wave equations implicative of finite propagation velocity and the unitarity and or composition series of associated actions of g general spin bundles on m are treated parallelized and correlated with bundles on m 0 associated covariant wave equations and the spectral resolution of fundamental quantum numbers are studied in detail in the scalar case

a pilot model in two dimensions for conformally invariant particle theory abstract the two dimensional analog of the mathematical model for elementary particles treated in this journal vol 75 1 57 is developed with greater explicitness than in the four dimensional case preliminary to quantization in part i the section space of the complex spannor bundle is studied invariant subspaces invariant forms and irreducible positive energy factors under the connected conformal group are determined transformation properties under discrete symmetries are also treated relations to the spinor bundle are treated the dirac operator is a canonical transform of the quadratic casimir on the spannor bundle and the section spaces have the same invariant factors at the same time the spinors constitute a deformation of the spannors two natural parallelizations of the spannor bundle and their intertwining operator are computed the irreducible factors of the spannor section space under the conformal group are determined by their restrictions to minkowski space and this group acts continuously in the l2 topology in contrast to its action on the spinor section space

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

semi blind data detection for unitary space time modulation in mimo communications systems we propose an iterative algorithm based on expectation maximization em to jointly estimate the system parameters and decode the data in a mimo system using unitary space time block codes it is assumed that the receiver is unaware of the channel coefficients and their distribution the average energy of the received signal the prior probability of each signal in the constellation and the noise power the algorithm works for arbitrary modulation schemes and any channel model including rayleigh and rician fading the complexity of the proposed receiver is computed and it is shown to be significantly lower than previously published methods as it does not require any matrix inversion or trellis search the performance of the proposed receiver is evaluated by simulations in terms of symbol error rate ser vs signal to noise ratio snr and it is shown that with only a few iterations of the algorithm it achieves a performance close to that of the receiver which knows all the parameters

complex symmetric composition operators on the newton space abstract a conjecture posed by macdonald and rosenthal states the composition operator c acting on the newton space n 2 p induced by z m z m 1 2 is bounded where m 0 1 our first result is proving that the aforementioned conjecture holds we investigate complex symmetry of composition operators acting on the newton space which is different from that on the hardy space in addition normality and co isometry of composition operators are studied finally we consider complex symmetric weighted composition operators

complex symmetric composition operators on a hilbert space of dirichlet series abstract on the hilbert space of dirichlet series with square summable coefficients there are no non normal complex symmetric composition operators induced by non constant symbols this is in sharp contrast with the phenomenon on the classical hardy space over the unit disk

analysis in space time bundles ii the spinor and form bundles abstract the structures of the spin and form bundles over the universal cosmos m and their relations with corresponding bundles over the minkowski space m 0 canonically imbedded in m are treated wave equations covariant with respect to the causal group g of m are studied their solution manifolds and other stable essentially positive energy invariant subspaces of the section spaces of the bundles are determined and the indecomposability of relevant invariant subspace chains is shown explicit parallelizations of the bundles are applied to the dirac and maxwell equations on m a basis for spinor fields that diagonalizes a complete set of k covariant quantum numbers k maximal essentially compact subgroup of g is developed local multilinear invariants of bundles over m are treated and specialized to convergent mathematical versions of the fermi and yukawa interaction lagrangians that are g invariant for the appropriate conformal weights

conformal extension of massive wave functions abstract we extend from the massless to the massive case the canonical conformal mapping of solutions of wave equations in two dimensional minkowski space m 0 into the universal cover m of the conformal compactification m of m 0 there is a continuous poincare covariant map from the space of solutions of the klein gordon equation in m 0 to the dual of the space of analytic vectors for the action of the conformal group g su 1 1 su 1 1 on massive fields in m the extensions satisfy a corresponding wave equation in m as in the case of massless equations the extended solutions are periodic under the generator of the infinite cyclic center of the conformal group g in m the analysis involves the determination of the action of the chronometric temporal evolution i e the one parameter group of nonlinear transformations generated by the center of the maximal essentially compact subgroup of g on the fourier transforms of wave functions in minkowski space the analytic continuation of this evolution to complex times of positive imaginary part is represented by a hilbert schmidt operator whose kernel is determined in closed form fields of higher conformal weight associated with other discrete series representations of g are also treated in this respect

scattering and complete integrability in conformally invariant nonlinear theories conformally invariant nonlinear wave equations in four dimensions corresponding to multicomponent massless scalar fields with a quartic interaction are studied it is proved that the scattering operator s on the space h of finite einstein energy cauchy data has infinitely many fixed points as well as periodic points of all orders there are also h such that sn is almost periodic but not periodic and h such that sn is not almost periodic it is also proved that h admits no conformally invariant kahler metrics but infinitely many distinct kahler metrics invariant under the poincare group and scale transformations moreover it is proved that time evolution for these nonlinear wave equations is completely integrable on the space h

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length

the global goursat problem and scattering for nonlinear wave equations abstract the goursat problem for nonlinear scalar equations on the einstein universe m with finite energy datum has a unique global solution in the positive energy sobolev controllable case such equations include those of the form h 0 where h denotes a hamiltonian that is a fourth order polynomial bounded below in components of the multicomponent scalar section in particular the conformally invariant equation 1 3 0 0 is included in the higher dimensional analog r s n to the einstein universe the same result holds under the stronger conditions on h required for sobolev controllability irrespective of energy positivity there is a unique local in time solution for arbitrary finite energy goursat datum for all n 3 establishing evolution from the given lightcone to any sufficiently close lightcone these results show the existence of wave operators in the sense of scattering theory and their continuity in the einstein energy metric for positive energy equations of the indicated type they also permit the comprehensive reduction of scattering theory for conformally invariant wave equations in minkowski space m 0 to the goursat problem in m in particular any solution of the equation arising from a nonnegative conformally invariant biquadratic interaction lagrangian on multicomponent scalar sections having finite einstein energy at any one time is asymptotic to solutions of the corresponding multicomponent free wave equation as the minkowski time x 0 thus given a finite einstein energy solution of the equation 3 0 on m 0 0 there exist unique solutions of the free wave equation which approach in the minkowski energy norm as x 0 and every finite einstein energy solution of the free wave equation is of the form or for a unique solution of the nonlinear equation this generalizes in part in maximality sharp form earlier results of strauss for this equation

sequence estimation in the presence of random parameters via the em algorithm the expectation maximization em algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum likelihood hit parameter estimates in this paper we investigate the application of the em algorithm to sequence estimation in the presence of random disturbances and additive white gaussian noise as examples of the use of the em algorithm we look at the random phase and fading channels and show that a formulation of the sequence estimation problem based on the em algorithm can provide a means of obtaining ml sequence estimates a task that has been previously too complex to perform