Publication:
Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/32474
ISSN: 1422-6383
DOI: https://doi.org/10.1007/s00025-020-1164-y
UXXI: AR/0000025589
Files
convolution_RM_2020_ps.pdf (282.32 KB)
Publication date
2020-02-05
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
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.
Description
Keywords
Convolution systems, Discrete abelian groups, Dual frames, Sampling expansion, Unitary representation of a group
Bibliographic citation
Results in Mathematics, (2020), v. 75, Article number: 40.
Collections
DM - AMCSS - Artículos de Revistas