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2015-10-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/67005

Uniformly bounded orthonormal polynomials on the sphere 

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http://dx.doi.org/10.1112/blms/bdv061

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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Funcions holomorfes, Funcions de diverses variables complexes, Espais fibrats (Matemàtica)

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Holomorphic functions, Functions of several complex variables, Fiber spaces (Mathematics)

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MARZO SÁNCHEZ, Jordi and ORTEGA CERDÀ, Joaquim. Uniformly bounded orthonormal polynomials on the sphere . Bulletin of the London Mathematical Society. 2015. Vol. 47, num. 5, pags. 883-891. ISSN 0024-6093. [consulted: 16 of June of 2026]. Available at: https://hdl.handle.net/2445/67005

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