Asymptotic properties of Gabor frame operators as sampling density tends to infinity

DOI10.1016/j.jfa.2009.09.018zbMath1198.42031OpenAlexW2033942185MaRDI QIDQ1048190

Wen-chang Sun

Publication date: 11 January 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.09.018

zbMATH Keywords

windowed Fourier transformframe operatorGabor framesynthesis operatorWalnut's representation

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20)

Related Items (17)

New inequalities of \(K\)-g-frames in submodules ⋮ A new inequality for frames in Hilbert spaces ⋮ Some notes on weaving frames in Hilbert spaces ⋮ Inversion Formula for Shearlet Transform in Arbitrary Space Dimensions ⋮ On \(K\)-duality and redundancy of \(K\)-g-frames ⋮ Convergence of wavelet frame operators as the sampling density tends to infinity ⋮ Inversion formula for the windowed Fourier transform. II ⋮ Invertibility of g-frame multipliers and Bessel multipliers for unitary systems in Hilbert C*-modules ⋮ Some new inequalities for K-frames ⋮ Canonical dual \(K\)-g-Bessel sequences and \(K\)-g-frame sequences ⋮ Convergence of Riemannian sums of inverse wavelet transforms ⋮ Sampling approximation by framelets in Sobolev space and its application in modifying interpolating error ⋮ Behavior of Gabor frame operators on Wiener amalgam spaces ⋮ On \(K\)-frame generators for unitary systems in Hilbert \(C^\ast\)-modules ⋮ Some properties of canonical dual \(K\)-Bessel sequences for Parseval \(K\)-frames ⋮ New types of inequalities for fusion frames ⋮ Some New Results of Weaving K-Frames in Hilbert Spaces

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• Ten Lectures on Wavelets
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