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arXiv · 1108.6108

Multi-window Gabor frames in amalgam spaces

Radu Balan·Jens G. Christensen·Ilya A. Krishtal·Kasso A. Okoudjou·José Luis Romero
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Abstract

We show that multi-window Gabor frames with windows in the Wiener algebra $W(L^{\infty}, \ell^{1})$ are Banach frames for all Wiener amalgam spaces. As a byproduct of our results we positively answer an open question that was posed by [Krishtal and Okoudjou, Invertibility of the Gabor frame operator on the Wiener amalgam space, J. Approx. Theory, 153(2), 2008] and concerns the continuity of the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra. The proofs are based on a recent version of Wiener's $1/f$ lemma.

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Radu Balan, Jens G. Christensen, Ilya A. Krishtal, Kasso A. Okoudjou, José Luis Romero. 2011-08-31. Multi-window Gabor frames in amalgam spaces. https://doi.org/10.4310/mrl.2014.v21.n1.a4

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