Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications

We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the a...

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Detalles Bibliográficos
Autores principales:	Heineken, Sigrid Bettina, Paternostro, Victoria
Publicado:	2014
Materias:	Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Riesz basis Vector spaces Hilbert spaces
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v12_n2_p_Heineken http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_02196913_v12_n2_p_Heineken
record_format	dspace
spelling	paper:paper_02196913_v12_n2_p_Heineken2023-06-08T15:21:39Z Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications Heineken, Sigrid Bettina Paternostro, Victoria Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces. © 2014 World Scientific Publishing Company. Fil:Heineken, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v12_n2_p_Heineken http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces
spellingShingle	Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces Heineken, Sigrid Bettina Paternostro, Victoria Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
topic_facet	Approximate reconstructions Bandlimited functions Canonical duals Frames Irregular translates Riesz bases Band-limited functions Canonical duals Frames Irregular translates Riesz basis Vector spaces Hilbert spaces
description	We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces. © 2014 World Scientific Publishing Company.
author	Heineken, Sigrid Bettina Paternostro, Victoria
author_facet	Heineken, Sigrid Bettina Paternostro, Victoria
author_sort	Heineken, Sigrid Bettina
title	Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_short	Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_full	Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_fullStr	Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_full_unstemmed	Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
title_sort	perturbed frame sequences: canonical dual systems, approximate reconstructions and applications
publishDate	2014
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v12_n2_p_Heineken http://hdl.handle.net/20.500.12110/paper_02196913_v12_n2_p_Heineken
work_keys_str_mv	AT heinekensigridbettina perturbedframesequencescanonicaldualsystemsapproximatereconstructionsandapplications AT paternostrovictoria perturbedframesequencescanonicaldualsystemsapproximatereconstructionsandapplications
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Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications

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