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Fernández Morales, Héctor Raúl and García, A.G. and Hernandez Medina, Miguel Angel and Muñoz Bouzo, María José (2015). Generalized sampling: from shift-invariant to U-invariant spaces. "Analysis and Applications", v. 13 (n. 3); pp. 303-329. ISSN 0219-5305. https://doi.org/10.1142/S0219530514500213.
Title: | Generalized sampling: from shift-invariant to U-invariant spaces |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Analysis and Applications |
Date: | May 2015 |
ISSN: | 0219-5305 |
Volume: | 13 |
Subjects: | |
Freetext Keywords: | Stationary sequences; U-invariant subspaces; frames; dual frames; time-jitter error; group of unitary operators; pseudo-dual frames |
Faculty: | E.T.S.I. Telecomunicación (UPM) |
Department: | Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones |
Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
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The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.
Type | Code | Acronym | Leader | Title |
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Government of Spain | MTM 2009-08345 | Unspecified | Unspecified | Aproximación mediante fórmulas de muestreo en espacios invariantes por traslación: Aplicaciones |
Item ID: | 41212 |
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DC Identifier: | https://oa.upm.es/41212/ |
OAI Identifier: | oai:oa.upm.es:41212 |
DOI: | 10.1142/S0219530514500213 |
Official URL: | http://www.worldscientific.com/doi/abs/10.1142/S0219530514500213 |
Deposited by: | Memoria Investigacion |
Deposited on: | 29 Jun 2016 17:03 |
Last Modified: | 29 Jun 2016 17:03 |