MULTI-WINDOW GABOR FRAMES IN AMALGAM SPACES

Radu Balan; Jens G. Christensen; Ilya A. Krishtal; Kasso A. Okoudjou; Jose Luis Romero

doi:10.4310/MRL.2014.v21.n1.a4

MULTI-WINDOW GABOR FRAMES IN AMALGAM SPACES

Radu Balan, Jens G. Christensen, Ilya A. Krishtal, Kasso A. Okoudjou, Jose Luis Romero

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We show that multi-window Gabor frames with windows in the Wiener algebra W(L∞,ℓ1) 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.

Original language	English
Pages (from-to)	55-69
Number of pages	15
Journal	Mathematical Research Letters
Volume	21
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2014.v21.n1.a4
Publication status	Published - 2014

Austrian Fields of Science 2012

101002 Analysis

Keywords

Wiener amalgam space
Gabor frame
Wiener's Lemma
WIENERS LEMMA
BANACH FRAMES
OPERATOR
APPROXIMATION
INVERTIBILITY
LOCALIZATION
EXPANSIONS

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10.4310/MRL.2014.v21.n1.a4

http://arxiv.org/pdf/1108.6108

Cite this

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title = "MULTI-WINDOW GABOR FRAMES IN AMALGAM SPACES",

abstract = "We show that multi-window Gabor frames with windows in the Wiener algebra W(L∞,ℓ1) 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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doi = "10.4310/MRL.2014.v21.n1.a4",

language = "English",

volume = "21",

pages = "55--69",

journal = "Mathematical Research Letters",

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AU - Balan, Radu

AU - Christensen, Jens G.

AU - Krishtal, Ilya A.

AU - Okoudjou, Kasso A.

AU - Romero, Jose Luis

PY - 2014

Y1 - 2014

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AB - We show that multi-window Gabor frames with windows in the Wiener algebra W(L∞,ℓ1) 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.

KW - Wiener amalgam space

KW - Gabor frame

KW - Wiener's Lemma

KW - WIENERS LEMMA

KW - BANACH FRAMES

KW - OPERATOR

KW - APPROXIMATION

KW - INVERTIBILITY

KW - LOCALIZATION

KW - EXPANSIONS

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DO - 10.4310/MRL.2014.v21.n1.a4

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SN - 1073-2780

VL - 21

SP - 55

EP - 69

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 1

ER -

MULTI-WINDOW GABOR FRAMES IN AMALGAM SPACES

Abstract

Austrian Fields of Science 2012

Keywords

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