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Knit product of finite groups and sampling
Citation
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.
Description
| Title: | Knit product of finite groups and sampling |
|---|---|
| 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 |
Abstract
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.
Funding Projects
Type
Code
Acronym
Leader
Title
Government of Spain
MTM2017-84098-P
Unspecified
Unspecified
Fundamentos matemáticos de las tecnologías de la información cuánticas: convexidad, muestreo y algebras de operadores
More information
| Item ID: | 64003 |
|---|---|
| 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 |
