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dc.contributor.author
Cabrelli, Carlos
dc.contributor.author
Mosquera, Carolina Alejandra
dc.contributor.author
Paternostro, Victoria
dc.date.available
2018-08-14T19:05:28Z
dc.date.issued
2017-07
dc.identifier.citation
Cabrelli, Carlos; Mosquera, Carolina Alejandra; Paternostro, Victoria; An approximation problem in multiplicatively invariant spaces; American Mathematical Society; Contemporary Mathematics; 693; 7-2017; 1-23
dc.identifier.issn
0271-4132
dc.identifier.uri
http://hdl.handle.net/11336/55464
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Shift-Invariant Spaces
dc.subject
Extra Invariance
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Multiplicatively Invariant Spaces
dc.subject
Approximation.
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
An approximation problem in multiplicatively invariant spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-14T13:58:07Z
dc.journal.volume
693
dc.journal.pagination
1-23
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
dc.description.fil
Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
dc.description.fil
Fil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
dc.journal.title
Contemporary Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/693/
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1602.08608
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