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García García, Antonio, Hernández Medina, Miguel Ángel ORCID: https://orcid.org/0000-0002-0722-1055 and Ibort Latre, Alberto
(2019).
Knit product of finite groups and sampling.
"Mediterranean Journal of Mathematics", v. 16
(n. 146);
pp. 1-15.
ISSN 1660-5446.
https://doi.org/10.1007/s00009-019-1417-8.
Title: | Knit product of finite groups and sampling |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Mediterranean Journal of Mathematics |
Date: | October 2019 |
ISSN: | 1660-5446 |
Volume: | 16 |
Subjects: | |
Freetext Keywords: | Knit product of groups; unitary representation of a group; finite unitary-invariant subspaces; finite frames; dual frames; left-inverses; sampling expansions |
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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A finite sampling theory associated with a unitary representation of a finite non-abelian group G on a Hilbert space is established. The non-abelian group G is a knit product of two finite subgroups N and H where at least N or H is abelian. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space l2(G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results.
Item ID: | 64003 |
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DC Identifier: | https://oa.upm.es/64003/ |
OAI Identifier: | oai:oa.upm.es:64003 |
DOI: | 10.1007/s00009-019-1417-8 |
Official URL: | https://link.springer.com/article/10.1007/s00009-0... |
Deposited by: | Memoria Investigacion |
Deposited on: | 06 Dec 2020 09:42 |
Last Modified: | 06 Dec 2020 09:42 |