Convergence and summability of Gabor expansions at the Nyquist density

DOI10.1007/BF01261606zbMath0936.42016MaRDI QIDQ1293825

Kristian Seip, Yurij I. Lyubarskij

Publication date: 16 January 2000

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59601

zbMATH Keywords

waveletsuncertainty principleHilbert scalesGabor expansionsNyquist densityBargmann scaleSchwartz scale

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Special methods of summability (40G99) Representations of entire functions of one complex variable by series and integrals (30D10)

Related Items

Gabor (super)frames with Hermite functions, Uniqueness of Gabor series, Gabor frame bound optimizations, Zero-based subspaces and quasi-invariant subspaces of the Bargmann-Fock space, On a characterization of Riesz bases via biorthogonal sequences, Summability properties of Gabor expansions, A stability problem for some complete and minimal Gabor systems in $L^2(\mathbb {R})$, Some curious results related to a conjecture of Strohmer and Beaver, Summability of Gabor expansions and Hardy spaces, On representation of functions from normed subspaces of \(H(D)\) by series of exponentials, Multivariate Gabor frames and sampling of entire functions of several variables, Frame constants of Gabor frames near the critical density, Phase space distribution of Gabor expansions, Pointwise summability of Gabor expansions

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