Reproducing Formulas and Double Orthogonality in Bargmann and Bergman Spaces

DOI10.1137/0522054zbMath0767.44005OpenAlexW2074529324MaRDI QIDQ3978305

Kristian Seip

Publication date: 25 June 1992

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0522054

zbMATH Keywords

waveletseigenvalueseigenvectorseigenfunctionsBergman spacesreproducing kernelssampling theoremprolate spheroidal wave functionssignal analysisBargmann spacesreproducing formulasconcentration operatorsdouble orthogonality

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) General harmonic expansions, frames (42C15) Interpolation in approximation theory (41A05) Communication theory (94A05) Kernel functions in one complex variable and applications (30C40)

Related Items (18)

Restriction operators, balayage and doubly orthogonal systems of analytic functions ⋮ Density theorems for sampling and interpolation \\ in the Bargmann-Fock space ⋮ The norm of time-frequency and wavelet localization operators ⋮ Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles ⋮ A Faber–Krahn inequality for Wavelet transforms ⋮ Sharp rates of convergence for accumulated spectrograms ⋮ Remarks on isometric mappings between the Hardy–Szegö and Bergman–Selberg spaces: wavelet transforms and Laguerre functions ⋮ Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions ⋮ Landau's necessary density conditions for the Hankel transform ⋮ Dilation of the Weyl symbol and Balian-Low theorem ⋮ Interpolating sequences for Bargmann-Fock spaces in \(\mathbb C^n\) ⋮ Sampling in weighted \(L^p\) spaces of entire functions in \(\mathbb{C}^n\) and estimates of the Bergman kernel ⋮ Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions ⋮ Regular Sets of Sampling and Interpolation for Weighted Bergman Spaces ⋮ Planar sampling sets for the short-time Fourier transform ⋮ Donoho-Logan large sieve principles for modulation and polyanalytic Fock spaces ⋮ A fractal uncertainty principle for Bergman spaces and analytic wavelets ⋮ Measures of localization and quantitative Nyquist densities

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