RT Journal Article
T1 Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory
A1 García García, Antonio
A1 Hernández Medina, Miguel Ángel
A1 Pérez Villalón, Gerardo
AB A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space H is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group G on H. The samples are defined by means of a filtering process which generalizes the usual sampling settings. The multiply generated setting allows to consider some examples where the group G is non-abelian as, for instance, crystallographic groups. Finally, it is worth to mention that classical average or pointwise sampling in shift-invariant subspaces are particular examples included in the followed approach.
PB Springer
SN 1422-6383
YR 2020
FD 2020-02-05
LK https://hdl.handle.net/10016/32474
UL https://hdl.handle.net/10016/32474
LA eng
NO This work has been supported by the grant MTM2017-84098-P from the Spanish Ministerio de Economía y Competitividad (MINECO).
DS e-Archivo
RD 27 jul. 2024