Sampling associated with a unitary representation of a semi-direct product of groups: A filter bank approach

García García, Antonio and Hernández Medina, Miguel Ángel and Pérez Villalón, Gerardo (2019). Sampling associated with a unitary representation of a semi-direct product of groups: A filter bank approach. "Symmetry-Basel", v. 11 (n. 4); pp. 1-15. ISSN 2073-8994. https://doi.org/10.3390/sym11040529.

Description

Title: Sampling associated with a unitary representation of a semi-direct product of groups: A filter bank approach
Author/s:
  • García García, Antonio
  • Hernández Medina, Miguel Ángel
  • Pérez Villalón, Gerardo
Item Type: Article
Título de Revista/Publicación: Symmetry-Basel
Date: 12 April 2019
ISSN: 2073-8994
Volume: 11
Subjects:
Freetext Keywords: semi-direct product of groups; unitary representation of a group; LCA groups; dualframes; 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

An abstract sampling theory associated with a unitary representation of a countable discrete non abelian group G, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples, the use of a filter bank formalism and the corresponding frame analysis allow for fixing the mathematical problem to be solved: the search of appropriate dual frames for l2(G). An example involving crystallographic groups illustrates the obtained results by using either average or pointwise samples.

Funding Projects

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

More information

Item ID: 64002
DC Identifier: http://oa.upm.es/64002/
OAI Identifier: oai:oa.upm.es:64002
DOI: 10.3390/sym11040529
Official URL: https://www.mdpi.com/2073-8994/11/4/529
Deposited by: Memoria Investigacion
Deposited on: 05 Oct 2020 14:32
Last Modified: 05 Oct 2020 14:32
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