Generalized sampling: from shift-invariant to U-invariant spaces

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.

Description

Title: Generalized sampling: from shift-invariant to U-invariant spaces
Author/s:
  • Fernández Morales, Héctor Raúl
  • García, A.G.
  • Hernandez Medina, Miguel Angel
  • Muñoz Bouzo, María José
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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Abstract

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.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM 2009-08345UnspecifiedUnspecifiedAproximación mediante fórmulas de muestreo en espacios invariantes por traslación: Aplicaciones

More information

Item ID: 41212
DC Identifier: http://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
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