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

García García, Antonio, Hernández Medina, Miguel Ángel ORCID: https://orcid.org/0000-0002-0722-1055 and Pérez Villalón, Gerardo ORCID: https://orcid.org/0000-0003-2061-917X (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:
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

Type
Code
Acronym
Leader
Title
Government of Spain
MTM2017-84098-P
MINECO
Unspecified
Fundamentos matemáticos de las tecnologías de la información cuánticas: convexidad, muestreo y algebras de operadores

More information

Item ID: 64002
DC Identifier: https://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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