RT Journal Article
T1 Generalized sampling: from shift-invariant to U-invariant spaces
A1 Fernández Morales, Héctor Raúl
A1 García García, Antonio
A1 Hernández Medina, Miguel Ángel
A1 Muñoz-Bouzo, María José
AB 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.
PB World Scientific Publishing
SN 0219-5305
YR 2015
FD 2015-05-01
LK https://hdl.handle.net/10016/36166
UL https://hdl.handle.net/10016/36166
LA eng
NO The authors wish to thank the referees for their valuable and constructive comments. This work has been supported by the grant MTM2009-08345 from the Spanish Ministerio de Ciencia e Innovación (MICINN)
DS e-Archivo
RD 1 sept. 2024