Behavior of Gabor frame operators on Wiener amalgam spaces

Anirudha Poria

doi:10.1142/S0219691316500284

Behavior of Gabor frame operators on Wiener amalgam spaces

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Indian Institute of Technology Guwahati

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

It is well-known that the Gabor expansions converge to identity operator in weak∗sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak∗sense on W(L^p,ℓ^q) as the sampling density tends to infinity. Also we show the validity of the Janssen's representation and the Wexler-Raz biorthogonality condition for Gabor frame operator on W(L^p,ℓ^q).

Original language	English
Article number	1650028
Journal	International Journal of Wavelets, Multiresolution and Information Processing
Volume	14
Issue number	4
DOIs	https://doi.org/10.1142/S0219691316500284
Publication status	Published - 1 Jul 2016

Keywords

frame operator
Gabor frame
Janssen's representation
sampling density
Walnut's representation
Wexler-Raz biorthogonality relations
Wiener amalgam spaces
windowed Fourier transform

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abstract = "It is well-known that the Gabor expansions converge to identity operator in weak∗sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak∗sense on W(Lp,ℓq) as the sampling density tends to infinity. Also we show the validity of the Janssen's representation and the Wexler-Raz biorthogonality condition for Gabor frame operator on W(Lp,ℓq).",

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AB - It is well-known that the Gabor expansions converge to identity operator in weak∗sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak∗sense on W(Lp,ℓq) as the sampling density tends to infinity. Also we show the validity of the Janssen's representation and the Wexler-Raz biorthogonality condition for Gabor frame operator on W(Lp,ℓq).

KW - frame operator

KW - Gabor frame

KW - Janssen's representation

KW - sampling density

KW - Walnut's representation

KW - Wexler-Raz biorthogonality relations

KW - Wiener amalgam spaces

KW - windowed Fourier transform

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SN - 0219-6913

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JO - International Journal of Wavelets, Multiresolution and Information Processing

JF - International Journal of Wavelets, Multiresolution and Information Processing

IS - 4

M1 - 1650028

ER -

Behavior of Gabor frame operators on Wiener amalgam spaces

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Keywords

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