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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/135496
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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