JH-singularity and JH-regularity of multivariate stationary processes over LCA groups

Autores
Klotz, Lutz Peter; Medina, Juan Miguel
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let G be an LCA group, I' its dual group, and H a closed subgroup of G such that its annihilator is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on I' and L^2(M) the corresponding Hilbert space of matrix-valued functions square-integrable with respect to M. For g ϵ G, let Z_g be the closure in L^2(M) of all matrix-valued trigonometric polynomials with frequencies from g+H. We describe those measures M for which Z_g = L^2(M) as well as those for which ∩ gϵG Zg = {0}. Interpreting M as a spectral measure of a multivariate wide sense stationary processon G and denoting by J_H the family of H-cosets we obtain conditions forJ_H-singularity and JH-regularity.
Fil: Klotz, Lutz Peter. Universitat Leipzig; Alemania
Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
Materia
JH-REGULARITY
JH-SINGULARITY
LCA GROUP
MULTIVARIATE STATIONARY PROCESS
POSITIVE SEMIDEFINITE MATRIX-VALUED MEASURE
SAMPLING
TRIGONOMETRIC APPROXIMATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/135496

id CONICETDig_49045110b15b9388eb515988e1458cbc
oai_identifier_str oai:ri.conicet.gov.ar:11336/135496
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling JH-singularity and JH-regularity of multivariate stationary processes over LCA groupsKlotz, Lutz PeterMedina, Juan MiguelJH-REGULARITYJH-SINGULARITYLCA GROUPMULTIVARIATE STATIONARY PROCESSPOSITIVE SEMIDEFINITE MATRIX-VALUED MEASURESAMPLINGTRIGONOMETRIC APPROXIMATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let G be an LCA group, I' its dual group, and H a closed subgroup of G such that its annihilator is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on I' and L^2(M) the corresponding Hilbert space of matrix-valued functions square-integrable with respect to M. For g ϵ G, let Z_g be the closure in L^2(M) of all matrix-valued trigonometric polynomials with frequencies from g+H. We describe those measures M for which Z_g = L^2(M) as well as those for which ∩ gϵG Zg = {0}. Interpreting M as a spectral measure of a multivariate wide sense stationary processon G and denoting by J_H the family of H-cosets we obtain conditions forJ_H-singularity and JH-regularity.Fil: Klotz, Lutz Peter. Universitat Leipzig; AlemaniaFil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaKazimierz Urbanik Center for Probability and Mathematical Statistics2021-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/135496Klotz, Lutz Peter; Medina, Juan Miguel; JH-singularity and JH-regularity of multivariate stationary processes over LCA groups; Kazimierz Urbanik Center for Probability and Mathematical Statistics; Probability and Mathematical Statistics; 41; 1; 4-2021; 173-1920208-4147CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://math.uni.wroc.pl/~pms/publicationsArticle.php?doi=10.37190/0208-4147.41.1.11info:eu-repo/semantics/altIdentifier/doi/10.37190/0208-4147.41.1.11info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:47:14Zoai:ri.conicet.gov.ar:11336/135496instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:47:14.511CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
title JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
spellingShingle JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
Klotz, Lutz Peter
JH-REGULARITY
JH-SINGULARITY
LCA GROUP
MULTIVARIATE STATIONARY PROCESS
POSITIVE SEMIDEFINITE MATRIX-VALUED MEASURE
SAMPLING
TRIGONOMETRIC APPROXIMATION
title_short JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
title_full JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
title_fullStr JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
title_full_unstemmed JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
title_sort JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
dc.creator.none.fl_str_mv Klotz, Lutz Peter
Medina, Juan Miguel
author Klotz, Lutz Peter
author_facet Klotz, Lutz Peter
Medina, Juan Miguel
author_role author
author2 Medina, Juan Miguel
author2_role author
dc.subject.none.fl_str_mv JH-REGULARITY
JH-SINGULARITY
LCA GROUP
MULTIVARIATE STATIONARY PROCESS
POSITIVE SEMIDEFINITE MATRIX-VALUED MEASURE
SAMPLING
TRIGONOMETRIC APPROXIMATION
topic JH-REGULARITY
JH-SINGULARITY
LCA GROUP
MULTIVARIATE STATIONARY PROCESS
POSITIVE SEMIDEFINITE MATRIX-VALUED MEASURE
SAMPLING
TRIGONOMETRIC APPROXIMATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let G be an LCA group, I' its dual group, and H a closed subgroup of G such that its annihilator is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on I' and L^2(M) the corresponding Hilbert space of matrix-valued functions square-integrable with respect to M. For g ϵ G, let Z_g be the closure in L^2(M) of all matrix-valued trigonometric polynomials with frequencies from g+H. We describe those measures M for which Z_g = L^2(M) as well as those for which ∩ gϵG Zg = {0}. Interpreting M as a spectral measure of a multivariate wide sense stationary processon G and denoting by J_H the family of H-cosets we obtain conditions forJ_H-singularity and JH-regularity.
Fil: Klotz, Lutz Peter. Universitat Leipzig; Alemania
Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
description Let G be an LCA group, I' its dual group, and H a closed subgroup of G such that its annihilator is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on I' and L^2(M) the corresponding Hilbert space of matrix-valued functions square-integrable with respect to M. For g ϵ G, let Z_g be the closure in L^2(M) of all matrix-valued trigonometric polynomials with frequencies from g+H. We describe those measures M for which Z_g = L^2(M) as well as those for which ∩ gϵG Zg = {0}. Interpreting M as a spectral measure of a multivariate wide sense stationary processon G and denoting by J_H the family of H-cosets we obtain conditions forJ_H-singularity and JH-regularity.
publishDate 2021
dc.date.none.fl_str_mv 2021-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/135496
Klotz, Lutz Peter; Medina, Juan Miguel; JH-singularity and JH-regularity of multivariate stationary processes over LCA groups; Kazimierz Urbanik Center for Probability and Mathematical Statistics; Probability and Mathematical Statistics; 41; 1; 4-2021; 173-192
0208-4147
CONICET Digital
CONICET
url http://hdl.handle.net/11336/135496
identifier_str_mv Klotz, Lutz Peter; Medina, Juan Miguel; JH-singularity and JH-regularity of multivariate stationary processes over LCA groups; Kazimierz Urbanik Center for Probability and Mathematical Statistics; Probability and Mathematical Statistics; 41; 1; 4-2021; 173-192
0208-4147
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://math.uni.wroc.pl/~pms/publicationsArticle.php?doi=10.37190/0208-4147.41.1.11
info:eu-repo/semantics/altIdentifier/doi/10.37190/0208-4147.41.1.11
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Kazimierz Urbanik Center for Probability and Mathematical Statistics
publisher.none.fl_str_mv Kazimierz Urbanik Center for Probability and Mathematical Statistics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613472689586176
score 13.070432