Mathematical Research Letters

Volume 21 (2014)

Number 1

Multi-window Gabor frames in amalgam spaces

Pages: 55 – 69

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n1.a4

Authors

Radu Balan (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Jens G. Christensen (Department of Mathematics, Colgate University, Hamilton, New York, U.S.A.)

Ilya A. Krishtal (Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, U.S.A.)

Kasso A. Okoudjou (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

José Luis Romero (Faculty of Mathematics, University of Vienna, Austria)

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 by-product of our results we positively answer an open question that was posed by Krishtal and Okoudjou 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.

Keywords

Wiener amalgam space, Gabor frame, Wiener’s Lemma

2010 Mathematics Subject Classification

Primary 42C15. Secondary 42A65, 47B38.

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Published 25 July 2014