Representation and approximation of pseudodifferential operators by sums of Gabor multipliers

DOI10.1080/00036811.2010.499507zbMath1213.42108arXiv0908.2051OpenAlexW2114176901WikidataQ58255647 ScholiaQ58255647MaRDI QIDQ2995519

Karlheinz Gröchening

Publication date: 21 April 2011

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.2051

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Multipliers for harmonic analysis in several variables (42B15) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Pseudodifferential operators (47G30)

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Cites Work

• Banach spaces related to integrable group representations and their atomic decompositions. I
• Frame expansions for Gabor multipliers
• Representation of operators in the time-frequency domain and generalized Gabor multipliers
• Banach algebras of pseudodifferential operators and their almost diagonalization
• Gabor frames and time-frequency analysis of distributions
• Time-frequency analysis of localization operators.
• Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus
• Square integrable representations, von Neumann algebras and an application to Gabor analysis
• An algebra of pseudodifferential operators
• Pseudodifferential operators and Banach algebras in mobile communications
• Low-Complexity Equalization of OFDM in Doubly Selective Channels