the l2 boundedness of pseudodifferential operators on donne une nouvelle demonstration du theoreme de calderon vaillancourt on obtient la l 2 continuite de a x d si le symbole a x satisfait a certaines conditions

quantum variance and ergodicity for the baker s map we prove an egorov theorem or quantum classical correspondence for the quantised baker s map valid up to the ehrenfest time this yields a logarithmic upper bound for the decay of the quantum variance and as a corollary a quantum ergodic theorem for this map

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

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

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

lp and sobolev boundedness of pseudodifferential operators with non regular symbol a regularisation approach abstract in this paper we investigate l p and sobolev boundedness of a certain class of pseudodifferential operators with non regular symbols we employ regularisation methods namely convolution with a net of mollifiers e e and we study the corresponding net of pseudodifferential operators providing l p and sobolev estimates which relate the parameter e with the non regularity of the symbol

uncertainty principles as embeddings of modulation spaces abstract a class of new uncertainty principles is derived in the form of embeddings of fourier lebesgue spaces into modulation spaces these embeddings provide practical sufficient conditions for a function to belong to a modulation space counterexamples based on the properties of gabor expansions demonstrate that the embeddings are optimal

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

asymptotic density of eigenvalue clusters for the perturbed landau hamiltonian we consider the landau hamiltonian i e the 2d schrodinger operator with constant magnetic field perturbed by an electric potential v which decays sufficiently fast at infinity the spectrum of the perturbed hamiltonian consists of clusters of eigenvalues which accumulate to the landau levels applying a suitable version of the anti wick quantization we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity we obtain an explicit description of the asymptotic density of the eigenvalues in terms of the radon transform of the perturbation potential v

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

multilinear fourier multipliers related to time frequency localization we consider multilinear multipliers associated in a natural way with localization operators boundedness and compactness results are obtained in particular we get a geometric condition on a subset a r2d which guarantees that for a fixed synthesis window l2 rd the family of localization operators l a obtained when the analysis window varies on the unit ball of l2 rd is a relatively compact set of compact operators

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

annihilating sets for the short time fourier transform abstract we obtain a class of subsets of r 2 d such that the support of the short time fourier transform stft of a signal f l 2 r d with respect to a window g l 2 r d cannot belong to this class unless f or g is identically zero moreover we prove that the l 2 norm of the stft is essentially concentrated in the complement of such a set a generalization to other hilbert spaces of functions or distributions is also provided to this aim we obtain some results on compactness of localization operators acting on weighted modulation hilbert spaces

pseudodifferential operators on locally compact abelian groups and sjoestrand s symbol class we investigate pseudodifferential operators on arbitrary locally compact abelian groups as symbol classes for the kohn nirenberg calculus we introduce a version of sjoestrand s class pseudodifferential operators with such symbols form a banach algebra that is closed under inversion since hard analysis techniques are not available on locally compact abelian groups a new time frequency approach is used with the emphasis on modulation spaces gabor frames and banach algebras of matrices sjoestrand s original results are thus understood as a phenomenon of abstract harmonic analysis rather than hard analysis and are proved in their natural context and generality

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

harmonic analysis in phase space and finite weyl heisenberg ensembles weyl heisenberg ensembles are translation invariant determinantal point processes on mathbb r 2d associated with the schrodinger representation of the heisenberg group and include as examples the ginibre ensemble and the polyanalytic ensembles which model the higher landau levels in physics we introduce finite versions of the weyl heisenberg ensembles and show that they behave analogously to the finite ginibre ensembles more specifically guided by the observation that the ginibre ensemble with n points is asymptotically close to the restriction of the infinite ginibre ensemble to the disk of area n we define finite wh ensembles as adequate finite approximations of the restriction of infinite wh ensembles to a given domain omega we provide a precise rate for the convergence of the corresponding one point intensities to the indicator function of omega as omega is dilated and the process is rescaled proportionally thermodynamic regime the construction and analysis rely neither on explicit formulas nor on the asymptotics for orthogonal polynomials but rather on phase space methods second we apply our construction to study the pure finite ginibre type polyanalytic ensembles which model finite particle systems in a single landau level and are defined in terms of complex hermite polynomials on a technical level we show that finite wh ensembles provide an approximate model for finite polyanalytic ginibre ensembles and we quantify the corresponding deviation by means of this asymptotic description we derive estimates for the rate of convergence of the one point intensity of polyanalytic ginibre ensembles in the thermodynamic limit

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

c algebraic scattering theory and explicitly solvable quantum field theories a general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable but require the use of c algebraic techniques because time dependent scattering theory cannot be constructed in any one natural representation of the observable algebra the purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory in a setting free of other complications commonly associated with the specification of dynamics one of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations ccr the automorphism groups considered are induced by one parameter groups of symplectic transformations on the classical phase space over which the weyl algebra of the ccr is built each symplectic group is conjugate by a fixed

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

lp boundedness and compactness of localization operators abstract localization operators are special anti wick operators which arise in many fields of pure and applied mathematics we study in this paper some properties of two wavelet localization operators i e operators which depend on a symbol and two different windows in the case when the symbol f belongs to l p r 2 n we give an extension of some results proved by boggiatto and wong more precisely we obtain the boundedness and compactness of such operators on l q r n 2 p p 1 q 2 p p 1 for every p 1

model predictive control of multi rate sampled data systems a state space approach a model predictive control mpc technique is developed for systems with measurements available at different sampling rates the method uses general state space system representations that incorporate secondary measurements as well as primary measurements the optimal multi rate mr filtering method is used to develop prediction equations for mpc a simple suboptimal cascade filter is also proposed for dual rate dr systems where the primary measurements are available at a slow rate and the secondary measurements are available at a fast rate in addition to significant reduction in filter gain computation requirements the suboptimal filtering strategy offers superior primary measurement failure tolerance the applicability of the proposed methods to realistic systems is demonstrated through an example application to a high purity distillation column

improving computational efficiency of model predictive control algorithm using wavelet transformation we propose an mpc algorithm with desirable stability and constraint handling properties yet which retains computational simplicity the closed loop stability and constraint handling are achieved b

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

implementation of automorphism groups in certain representations of the canonical commutation relations necessary and sufficient conditions are given for the unitary implementability of one parameter unitary groups of one particle automorphisms of the ccr algebra in representations symplectically related to the fock representation the criteria become particularly simple when the one particle generator of the unitary group is positive and bounded away from zero in this case the automorphism group is unitarily implementable only in the representations unitarily equivalent to the fock representation if the spectrum of the generator includes zero however the situation is more complicated there then exist representations inequivalent to the fock representation which admit unitary implementation of the automorphism group it is also shown that whenever implementation of the automorphism group is possible the implementing operators can be chosen to be a strongly continuous unitary group guaranteeing the existence of a second quantized self adjoint generator

brief paper a state space gpc with extensions to multirate control a state space formulation for generalized predictive control gpc is presented unlike other state space formulations we derive both the state feedback controller and state estimator gains using a least squares framework the present formulation provides a set of consistent design choices for both the controller and the state estimator design it also encapsulates both single rate and multirate controllers in the same algorithm it is argued that such a design approach can be advantageous especially when the control algorithm is required to tolerate sensor failure the generality of the design method is illustrated by synthesizing two well known multirate control algorithms a link with the generalized sampled data hold function is also established