Perturbation techniques in irregular spline-type spaces

In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue...

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Detalles Bibliográficos
Autores principales:	Molter, Ursula Maria, Romero, José Luis
Publicado:	2008
Materias:	Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Set theory Perturbation techniques
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v6_n2_p249_Feichtinger http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_02196913_v6_n2_p249_Feichtinger
record_format	dspace
spelling	paper:paper_02196913_v6_n2_p249_Feichtinger2023-06-08T15:21:39Z Perturbation techniques in irregular spline-type spaces Molter, Ursula Maria Romero, José Luis Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Sampling Set theory Irregular sampling Nonuniform sampling Spline-type spaces Perturbation techniques In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue in the spirit of Kadec's Theorem for bandlimited functions (see Refs. 14 and 15). We further derive some quantitative estimates on the amount by which a sampling set can be perturbed, and finally prove a result on the existence of optimal perturbations (with the stability of reconstruction being the optimality criterion). Finally, the techniques developed in the earlier parts of the paper are used to study the problem of disturbing a basis for a spline-type space, in order to derive a sufficient criterion for a space generated by irregular translations to be a spline-type space. © 2008 World Scientific Publishing Company. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Romero, J.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v6_n2_p249_Feichtinger http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Sampling Set theory Irregular sampling Nonuniform sampling Spline-type spaces Perturbation techniques
spellingShingle	Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Sampling Set theory Irregular sampling Nonuniform sampling Spline-type spaces Perturbation techniques Molter, Ursula Maria Romero, José Luis Perturbation techniques in irregular spline-type spaces
topic_facet	Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Sampling Set theory Irregular sampling Nonuniform sampling Spline-type spaces Perturbation techniques
description	In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue in the spirit of Kadec's Theorem for bandlimited functions (see Refs. 14 and 15). We further derive some quantitative estimates on the amount by which a sampling set can be perturbed, and finally prove a result on the existence of optimal perturbations (with the stability of reconstruction being the optimality criterion). Finally, the techniques developed in the earlier parts of the paper are used to study the problem of disturbing a basis for a spline-type space, in order to derive a sufficient criterion for a space generated by irregular translations to be a spline-type space. © 2008 World Scientific Publishing Company.
author	Molter, Ursula Maria Romero, José Luis
author_facet	Molter, Ursula Maria Romero, José Luis
author_sort	Molter, Ursula Maria
title	Perturbation techniques in irregular spline-type spaces
title_short	Perturbation techniques in irregular spline-type spaces
title_full	Perturbation techniques in irregular spline-type spaces
title_fullStr	Perturbation techniques in irregular spline-type spaces
title_full_unstemmed	Perturbation techniques in irregular spline-type spaces
title_sort	perturbation techniques in irregular spline-type spaces
publishDate	2008
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v6_n2_p249_Feichtinger http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
work_keys_str_mv	AT molterursulamaria perturbationtechniquesinirregularsplinetypespaces AT romerojoseluis perturbationtechniquesinirregularsplinetypespaces
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Perturbation techniques in irregular spline-type spaces

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