Totally positive functions and Gabor frames over rational lattices

We show that for an arbitrary totally positive function g∈L1(R) and αβ rational, the Gabor family {e2πiβltg(t−αk):k,l∈Z} is a frame for L2(R), if and only if αβ

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-08, Vol.427, p.109113, Article 109113
Main Author: Gröchenig, Karlheinz
Format: Article
Language:English
Subjects:
Gabor frame
Invertibility of totally positive matrices
Spectral invariance
Totally positive function
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Summary:We show that for an arbitrary totally positive function g∈L1(R) and αβ rational, the Gabor family {e2πiβltg(t−αk):k,l∈Z} is a frame for L2(R), if and only if αβ
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109113