Time-Frequency Analysis of Sjöstrand's Class

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjostrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjostrand's fundamental results and to far-reaching generalizations

[1]  Kazuya Tachizawa,et al.  The Boundedness of Pseudodifferential Operators on Modulation Spaces , 2006 .

[2]  K. Gröchenig,et al.  Wiener's lemma for twisted convolution and Gabor frames , 2003 .

[3]  R. Beals.  Characterization of pseudodifferential operators and applications , 1977 .

[4]  A Boulkhemair,et al.  L2 Estimates for Weyl Quantization , 1999 .

[5]  K. Gröchenig,et al.  MODULATION SPACES AND A CLASS OF BOUNDED MULTILINEAR PSEUDODIFFERENTIAL OPERATORS , 2005 .

[6]  C. Heil,et al.  Singular Values of Compact Pseudodifferential Operators , 1997 .

[7]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[8]  Johannes Sj,et al.  AN ALGEBRA OF PSEUDODIFFERENTIAL OPERATORS , 1994 .

[9]  H. Feichtinger.  Modulation Spaces on Locally Compact Abelian Groups , 2003 .

[10]  Richard Rochberg,et al.  Pseudodifferential operators, Gabor frames, and local trigonometric bases , 1998 .

[11]  Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators , 1997 .

[12]  Wojciech Czaja,et al.  Boundedness of pseudodifferential operators on modulation spaces , 2003 .

[13]  Quantification asymptotique et microlocalisations d'ordre supérieur. I , 1987 .

[14]  S. Pilipovic,et al.  Pseudodifferential operators on ultra-modulation spaces , 2004 .

[15]  D. Walnut,et al.  Differentiation and the Balian-Low Theorem , 1994 .

[16]  D. Walnut.  Lattice size estimates for Gabor decompositions , 1993 .

[17]  J. Toft.  Continuity properties for modulation spaces, with applications to pseudo-differential calculus—I , 2004 .

[18]  J. Toft.  Positivity properties in noncommutative convoluti algebras with applications in pseudo-differential calculus , 2003 .

[19]  Lasse Borup,et al.  Pseudodifferential operators on a-modulation spaces , 2004 .

[20]  K. Hannabuss,et al.  HARMONIC ANALYSIS IN PHASE SPACE: (Annals of Mathematics Studies 122) , 1990 .

[21]  W. Czaja,et al.  Pseudodifferentia Operators and Gabor Frames: Spectral Asymptotics , 2002 .

[22]  G. Björck.  Linear partial differential operators and generalized distributions , 1966 .

[23]  Karlheinz Gröchenig,et al.  Modulation spaces and pseudodifferential operators , 1999 .

[24]  I. M. Gelfand,et al.  Commutative Normed Rings. , 1967 .

[25]  J. Toft,et al.  Subalgebras to a Wiener type algebra of pseudo-differential operators , 2006 .

[26]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[27]  A. Baskakov,et al.  Wiener's theorem and the asymptotic estimates of the elements of inverse matrices , 1990 .

[28]  F. Hérau.  Melin-Hörmander inequality in a Wiener type pseudo-differential algebra , 2001 .

[29]  Karlheinz Gröchenig,et al.  Counterexamples for boundedness of pseudodifferential operators , 2004 .

[30]  M. Shubin.  Pseudodifferential Operators and Spectral Theory , 1987 .

[31]  Karlheinz Gröchenig,et al.  Composition and spectral invariance of pseudodifferential Operators on Modulation Spaces , 2006 .

[32]  J. Sjöstrand,et al.  Wiener type algebras of pseudodifferential operators , 1995 .

[33]  MODULATION SPACES AS SYMBOL CLASSES FOR PSEUDODIFFERENTIAL OPERATORS , 2002 .

[34]  H. Feichtinger.  On a new Segal algebra , 1981 .

[35]  H. Feichtinger,et al.  Gabor Frames and Time-Frequency Analysis of Distributions* , 1997 .

[36]  A. Janssen.  Duality and Biorthogonality for Weyl-Heisenberg Frames , 1994 .

[37]  Demetrio Labate,et al.  Time-Frequency Analysis of Pseudodifferential Operators , 2001 .

[38]  K. Gröchenig,et al.  Time–Frequency analysis of localization operators , 2003 .

[39]  Massimo Fornasier,et al.  Intrinsic Localization of Frames , 2005 .