An approximation problem in multiplicatively invariant spaces

Autores
Cabrelli, Carlos; Mosquera, Carolina Alejandra; Paternostro, Victoria
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2(Ω, H), in this paper weprove the existence and construct an MI space M that best fits F, in the least squares sense. MIspaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve anapproximation problem for SI spaces in the context of locally compact abelian groups. On the otherhand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into anorthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces.Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we alsosolve our approximation problem for this class of SI spaces. Finally we prove that translation-invariantspaces are in correspondence with totally decomposable MI spaces.
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
Shift-Invariant Spaces
Extra Invariance
Multiplicatively Invariant Spaces
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:11336/55464
Acceder
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network_name_str CONICET Digital (CONICET)
spelling An approximation problem in multiplicatively invariant spacesCabrelli, CarlosMosquera, Carolina AlejandraPaternostro, VictoriaShift-Invariant SpacesExtra InvarianceMultiplicatively Invariant SpacesApproximation.https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2(Ω, H), in this paper weprove the existence and construct an MI space M that best fits F, in the least squares sense. MIspaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve anapproximation problem for SI spaces in the context of locally compact abelian groups. On the otherhand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into anorthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces.Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we alsosolve our approximation problem for this class of SI spaces. Finally we prove that translation-invariantspaces are in correspondence with totally decomposable MI spaces.Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaAmerican Mathematical Society2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55464Cabrelli, Carlos; Mosquera, Carolina Alejandra; Paternostro, Victoria; An approximation problem in multiplicatively invariant spaces; American Mathematical Society; Contemporary Mathematics; 693; 7-2017; 1-230271-4132CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/693/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1602.08608info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:16:06Zoai:ri.conicet.gov.ar:11336/55464instacron: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:34982025-10-22 11:16:06.766CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An approximation problem in multiplicatively invariant spaces
title An approximation problem in multiplicatively invariant spaces
spellingShingle An approximation problem in multiplicatively invariant spaces
Cabrelli, Carlos
Shift-Invariant Spaces
Extra Invariance
Multiplicatively Invariant Spaces
Approximation.
title_short An approximation problem in multiplicatively invariant spaces
title_full An approximation problem in multiplicatively invariant spaces
title_fullStr An approximation problem in multiplicatively invariant spaces
title_full_unstemmed An approximation problem in multiplicatively invariant spaces
title_sort An approximation problem in multiplicatively invariant spaces
dc.creator.none.fl_str_mv Cabrelli, Carlos
Mosquera, Carolina Alejandra
Paternostro, Victoria
author Cabrelli, Carlos
author_facet Cabrelli, Carlos
Mosquera, Carolina Alejandra
Paternostro, Victoria
author_role author
author2 Mosquera, Carolina Alejandra
Paternostro, Victoria
author2_role author
author
dc.subject.none.fl_str_mv Shift-Invariant Spaces
Extra Invariance
Multiplicatively Invariant Spaces
Approximation.
topic Shift-Invariant Spaces
Extra Invariance
Multiplicatively Invariant Spaces
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 H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2(Ω, H), in this paper weprove the existence and construct an MI space M that best fits F, in the least squares sense. MIspaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve anapproximation problem for SI spaces in the context of locally compact abelian groups. On the otherhand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into anorthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces.Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we alsosolve our approximation problem for this class of SI spaces. Finally we prove that translation-invariantspaces are in correspondence with totally decomposable MI spaces.
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2(Ω, H), in this paper weprove the existence and construct an MI space M that best fits F, in the least squares sense. MIspaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve anapproximation problem for SI spaces in the context of locally compact abelian groups. On the otherhand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into anorthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces.Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we alsosolve our approximation problem for this class of SI spaces. Finally we prove that translation-invariantspaces are in correspondence with totally decomposable MI spaces.
publishDate 2017
dc.date.none.fl_str_mv 2017-07
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/11336/55464
Cabrelli, Carlos; Mosquera, Carolina Alejandra; Paternostro, Victoria; An approximation problem in multiplicatively invariant spaces; American Mathematical Society; Contemporary Mathematics; 693; 7-2017; 1-23
0271-4132
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55464
identifier_str_mv Cabrelli, Carlos; Mosquera, Carolina Alejandra; Paternostro, Victoria; An approximation problem in multiplicatively invariant spaces; American Mathematical Society; Contemporary Mathematics; 693; 7-2017; 1-23
0271-4132
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/693/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1602.08608
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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
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score 12.982451

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