Knit product of finite groups and sampling

García García, Antonio and Hernández Medina, Miguel Ángel 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:
  • García García, Antonio
  • Hernández Medina, Miguel Ángel
  • Ibort Latre, Alberto
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

TypeCodeAcronymLeaderTitle
Government of SpainMTM2017-84098-PUnspecifiedUnspecifiedFundamentos matemáticos de las tecnologías de la información cuánticas: convexidad, muestreo y algebras de operadores

More information

Item ID: 64003
DC Identifier: http://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/s00009-019-1417-8
Deposited by: Memoria Investigacion
Deposited on: 06 Dec 2020 09:42
Last Modified: 06 Dec 2020 09:42
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