Zak transforms and Gabor frames of totally positive functions and exponential B-splines

DOI10.1016/j.jat.2014.05.010zbMath1291.42024arXiv1311.7359OpenAlexW2145185301MaRDI QIDQ2016140

Tobias Kloos, Joachim Stöckler

Publication date: 19 June 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.7359

zbMATH Keywords

total positivityZak transformGabor frameexponential B-spline

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) General harmonic expansions, frames (42C15) Spline approximation (41A15)

Related Items (16)

On the Gabor frame set for compactly supported continuous functions ⋮ Zeros of the Zak transform of averaged totally positive functions ⋮ On Gabor frames generated by sign-changing windows and B-splines ⋮ Totally positive functions and Gabor frames over rational lattices ⋮ Spline function generating Gabor systems on the half real line ⋮ Lipschitz continuity of spectra of pseudodifferential operators in a weighted Sjöstrand class and Gabor frame bounds ⋮ Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions ⋮ Counterexamples to the B-spline conjecture for Gabor frames ⋮ On some Hermite series identities and their applications to Gabor analysis ⋮ Gabor windows supported on \([- 1, 1\) and construction of compactly supported dual windows with optimal smoothness] ⋮ Zeros of the Zak transform of totally positive functions ⋮ Weighted Zak transforms and the dual tiling condition ⋮ Gabor Expansions of Signals: Computational Aspects and Open Questions ⋮ Frame sets for a class of compactly supported continuous functions ⋮ Totally positive functions in sampling theory and time-frequency analysis ⋮ On the frame set of the second-order B-spline

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