Modulation Spaces

DOI10.1007/978-1-0716-0332-1zbMath1476.35001OpenAlexW3008427995MaRDI QIDQ5207996

Publication date: 14 January 2020

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-0716-0332-1

zbMATH Keywords

embedding theorems Gabor frames time-frequency analysis Feichtinger algebra

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Pseudodifferential operators as generalizations of partial differential operators (35S05) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Multipliers for harmonic analysis in several variables (42B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Pseudodifferential operators (47G30) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02) Harmonic analysis and PDEs (42B37)

Related Items (33)

An Excursion to Multiplications and Convolutions on Modulation Spaces ⋮ Gabor frame characterizations of generalized modulation spaces ⋮ Equivalent norms for modulation spaces from positive Cohen's class distributions ⋮ Translation and modulation invariant Banach spaces of tempered distributions satisfy the metric approximation property ⋮ The inner kernel theorem for a certain Segal algebra ⋮ Norm inflation with infinite loss of regularity at general initial data for nonlinear wave equations in Wiener amalgam and Fourier amalgam spaces ⋮ Dual of modulation spaces with variable smoothness and integrability ⋮ Modulation spaces, multipliers associated with the special affine Fourier transform ⋮ New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis ⋮ Comparisons between Fourier and STFT multipliers: the smoothing effect of the short-time Fourier transform ⋮ Gabor frame bound optimizations ⋮ Gabor products and a phase space approach to nonlinear analysis ⋮ Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm ⋮ Efficient computation of the zeros of the Bargmann transform under additive white noise ⋮ Symplectic analysis of time-frequency spaces ⋮ Approximation by linear combinations of translates in invariant Banach spaces of tempered distributions via Tauberian conditions ⋮ Spectral deviation of concentration operators for the short-time Fourier transform ⋮ Special Fourier integral operators of types I and II with function-variable symbols: definition, relation to metaplectic transform, and Heisenberg's uncertainty principles ⋮ Characterization of modulation spaces by symplectic representations and applications to Schrödinger equations ⋮ Metaplectic Gabor frames and symplectic analysis of time-frequency spaces ⋮ Lipschitz continuity of spectra of pseudodifferential operators in a weighted Sjöstrand class and Gabor frame bounds ⋮ Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators ⋮ Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness ⋮ Completeness of shifted dilates in invariant Banach spaces of tempered distributions ⋮ Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces ⋮ Sampling trajectories for the short-time Fourier transform ⋮ Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces ⋮ Characterisation of the Weyl-Hörmander classes by time-frequency shifts ⋮ A note on operating functions of modulation spaces ⋮ On the existence of optimizers for time-frequency concentration problems ⋮ Wiener amalgam spaces of quasianalytic ultradistributions ⋮ Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type ⋮ Wigner analysis of operators. I: Pseudodifferential operators and wave fronts

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