A Riesz basis for Bargmann-Fock space related to sampling and interpolation

DOI10.1007/BF02384875zbMath0777.46029OpenAlexW2089003484MaRDI QIDQ2365891

David F. Walnut, Karlheinz Gröchening

Publication date: 29 June 1993

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02384875

zbMATH Keywords

reproducing kernelunconditional basisBargmann-Fock space of entire functionsWilson type bases

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of bounded analytic functions of one complex variable (30H05) Interpolation in approximation theory (41A05) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (11)

Density theorems for sampling and interpolation \\ in the Bargmann-Fock space ⋮ Beurling-type density criteria for system identification ⋮ Greedy bases in weighted modulation spaces ⋮ CHARACTERIZATION OF WILSON SYSTEMS FOR GENERAL LATTICES ⋮ Remarks on mapping properties for the Bargmann transform on modulation spaces ⋮ Lattice size estimates for Gabor decompositions ⋮ The Bargmann transform on modulation and Gelfand-Shilov spaces, with applications to Toeplitz and pseudo-differential operators ⋮ Mapping properties for the Bargmann transform on modulation spaces ⋮ Atomic decomposition for the harmonic Fock spaces in the plane ⋮ WILSON SYSTEM FOR TRIPLE REDUNDANCY ⋮ Symmetric Wilson systems

Cites Work

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• Hankel forms and the Fock space
• Gabor representation of generalized functions
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• On a Hilbert space of analytic functions and an associated integral transform part I
• Painless nonorthogonal expansions
• Frames in the bargmann space of entire functions
• Bargmann transform, Zak transform, and coherent states
• A Simple Wilson Orthonormal Basis with Exponential Decay
• The wavelet transform, time-frequency localization and signal analysis
• Harmonic Analysis in Phase Space. (AM-122)
• Wilson Bases and Modulation Spaces
• Continuous and Discrete Wavelet Transforms
• A Class of Nonharmonic Fourier Series

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