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2016 On Schauder basis properties of multiply generated Gabor systems
Morten Nielsen
Rocky Mountain J. Math. 46(6): 2043-2060 (2016). DOI: 10.1216/RMJ-2016-46-6-2043

Abstract

Let $\mathcal{A} $ be a finite subset of $L^2(\mathbb{R} )$ and $p,q\in \mathbb{N} $. We characterize the Schauder basis properties in $L^2(\mathbb{R} )$ of the Gabor system \[ G(1,p/q,\mathcal{A} )=\{e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z} , g\in \mathcal{A} \}, \] with a specific ordering on $\mathbb{Z} \times \mathbb{Z} \times \mathcal{A} $. The characterization is given in terms of a Muckenhoupt matrix $A_2$ condition on an associated Zibulski-Zeevi type matrix.

Citation

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Morten Nielsen. "On Schauder basis properties of multiply generated Gabor systems." Rocky Mountain J. Math. 46 (6) 2043 - 2060, 2016. https://doi.org/10.1216/RMJ-2016-46-6-2043

Information

Published: 2016
First available in Project Euclid: 4 January 2017

zbMATH: 1357.42034
MathSciNet: MR3591271
Digital Object Identifier: 10.1216/RMJ-2016-46-6-2043

Subjects:
Primary: 42C15 , 46B15
Secondary: ‎42C40

Keywords: conditional convergence , Muckenhoupt matrix condition , Multiple Gabor systems , Schauder basis

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 6 • 2016
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