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arXiv · 1801.10026

Gabor frames for model sets

Ewa Matusiak
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Abstract

We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the connection between model sets and almost periodic functions, as well as Poisson's summations formula for model sets we develop a form of a bracket product that plays a central role in our approach. Furthermore, we show that, if a Gabor system for a model set admits a dual which is of Gabor type, then the density of the model set has to be greater than one.

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Ewa Matusiak. 2018-01-27. Gabor frames for model sets. https://arxiv.org/abs/1801.10026

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