Rocky Mountain Journal of Mathematics

On Schauder basis properties of multiply generated Gabor systems

Morten Nielsen

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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.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 2043-2060.

Dates
First available in Project Euclid: 4 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1483520437

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-2043

Mathematical Reviews number (MathSciNet)
MR3591271

Zentralblatt MATH identifier
1357.42034

Subjects
Primary: 42C15: General harmonic expansions, frames 46B15: Summability and bases [See also 46A35]
Secondary: 42C40: Wavelets and other special systems

Keywords
Multiple Gabor systems Schauder basis Muckenhoupt matrix condition conditional convergence

Citation

Nielsen, Morten. On Schauder basis properties of multiply generated Gabor systems. Rocky Mountain J. Math. 46 (2016), no. 6, 2043--2060. doi:10.1216/RMJ-2016-46-6-2043. https://projecteuclid.org/euclid.rmjm/1483520437


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