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Title: Deformation of Gabor systems
Author: Gröchenig, Karlheinz
Ortega Cerdà, Joaquim
Romero, José Luis
Keywords: Anàlisi de Fourier
Anàlisi harmònica
Teoria d'operadors
Teoria quàntica
Teoria de la informació
Fourier analysis
Harmonic analysis
Operator theory
Quantum theory
Information theory
Issue Date: 4-Jun-2015
Publisher: Elsevier B.V.
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.
Note: Versió postprint del document publicat a:
It is part of: Advances in Mathematics, 2015, vol. 277, p. 388-425
Related resource:
ISSN: 0001-8708
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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