Gabor frames for rational functions
Peer reviewed, Journal article
Published version
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Åpne
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https://hdl.handle.net/11250/3061393Utgivelsesdato
2022Metadata
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- Institutt for matematiske fag [2440]
- Publikasjoner fra CRIStin - NTNU [38055]
Sammendrag
We study the frame properties of the Gabor systems
G(g;α,β):={e2πiβmxg(x−αn)}m,n∈Z.
In particular, we prove that for Herglotz windows g such systems always form a frame for L2(R)
if α,β>0, αβ≤1. For general rational windows g∈L2(R) we prove that G(g;α,β) is a frame for L2(R) if 0<α,β, αβ<1, αβ∉Q and g^(ξ)≠0, ξ>0, thus confirming Daubechies conjecture for this class of functions. We also discuss some related questions, in particular sampling in shift-invariant subspaces of L2(R).