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2015-06-04

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/65247

Deformation of Gabor systems

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http://dx.doi.org/10.1016/j.aim.2015.01.019

Abstract

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames 'without inequalities' from lattices to non-uniform sets.

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Anàlisi de Fourier, Anàlisi harmònica, Teoria d'operadors, Teoria quàntica, Teoria de la informació

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Fourier analysis, Harmonic analysis, Operator theory, Quantum theory, Information theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

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GRÖCHENIG, Karlheinz, ORTEGA CERDÀ, Joaquim and ROMERO, José Luis. Deformation of Gabor systems. Advances in Mathematics. 2015. Vol. 277, num. 388-425. ISSN 0001-8708. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/65247

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