Convolution systems on discrete abelian groups as a unifying strategy in sampling theory

Autor:	García, Antonio G., Hernández-Medina, Miguel A., Pérez-Villalón, Gerardo
Rok vydání:	2019
Předmět:	Mathematics - Functional Analysis 42C15 94A20 22B05 20H15
Druh dokumentu:	Working Paper
Popis:	A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on $\mathcal{H}$. 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. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.02999 Zobrazit plný text záznamu View this record from Arxiv