Rocky Mountain Journal of Mathematics

On Schauder basis properties of multiply generated Gabor systems

Morten Nielsen

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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

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

First available in Project Euclid: 4 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Multiple Gabor systems Schauder basis Muckenhoupt matrix condition conditional convergence


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.

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