Knit product of finite groups and sampling

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:
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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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
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