Approximation by crystal-refinable functions

Autores
Molter, Ursula Maria; Moure, María del Carmen; Quintero, Alejandro Daniel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let Γ be a crystal group in Rd. A function φ:Rd⟶C is said to be crystal-refinable (or Γ-refinable) if it is a linear combination of finitely many of the rescaled and translated functions φ(γ−1(ax)), where the translationsγ are taken on a crystal group Γ, and a is an expansive dilation matrix such that aΓa−1⊂Γ. A Γ-refinable function φ:Rd→C satisfies a refinement equation φ(x)=∑γ∈Γdγφ(γ−1(ax)) with dγ∈C. Let S(φ) be the linear span of {φ(γ−1(x)):γ∈Γ} and Sh={f(x/h):f∈S(φ)}. One important property of S(φ) is, how well it approximates functions in L2(Rd). This property is very closely related to the crystal-accuracy of S(φ), which is the highest degree p such that all multivariate polynomials q(x) of degree(q)
Fil: Molter, Ursula Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Moure, María del Carmen. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Quintero, Alejandro Daniel. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
CRYSTAL GROUPS
APPROXIMATION PROPERTY
COMPOSITE DILATIONS
REFINEMENT EQUATION
ACCURACY
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
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oai:ri.conicet.gov.ar:11336/136210
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Approximation by crystal-refinable functionsMolter, Ursula MariaMoure, María del CarmenQuintero, Alejandro DanielCRYSTAL GROUPSAPPROXIMATION PROPERTYCOMPOSITE DILATIONSREFINEMENT EQUATIONACCURACYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Γ be a crystal group in Rd. A function φ:Rd⟶C is said to be crystal-refinable (or Γ-refinable) if it is a linear combination of finitely many of the rescaled and translated functions φ(γ−1(ax)), where the translationsγ are taken on a crystal group Γ, and a is an expansive dilation matrix such that aΓa−1⊂Γ. A Γ-refinable function φ:Rd→C satisfies a refinement equation φ(x)=∑γ∈Γdγφ(γ−1(ax)) with dγ∈C. Let S(φ) be the linear span of {φ(γ−1(x)):γ∈Γ} and Sh={f(x/h):f∈S(φ)}. One important property of S(φ) is, how well it approximates functions in L2(Rd). This property is very closely related to the crystal-accuracy of S(φ), which is the highest degree p such that all multivariate polynomials q(x) of degree(q)Fil: Molter, Ursula Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Moure, María del Carmen. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Quintero, Alejandro Daniel. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2019-10-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/136210Molter, Ursula Maria; Moure, María del Carmen; Quintero, Alejandro Daniel; Approximation by crystal-refinable functions; Springer; Geometriae Dedicata; 207; 1; 24-10-2019; 1-210046-5755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10711-019-00483-9info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-019-00483-9info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1701.08226info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:10:26Zoai:ri.conicet.gov.ar:11336/136210instacron: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 10:10:27.285CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximation by crystal-refinable functions
title Approximation by crystal-refinable functions
spellingShingle Approximation by crystal-refinable functions
Molter, Ursula Maria
CRYSTAL GROUPS
APPROXIMATION PROPERTY
COMPOSITE DILATIONS
REFINEMENT EQUATION
ACCURACY
title_short Approximation by crystal-refinable functions
title_full Approximation by crystal-refinable functions
title_fullStr Approximation by crystal-refinable functions
title_full_unstemmed Approximation by crystal-refinable functions
title_sort Approximation by crystal-refinable functions
dc.creator.none.fl_str_mv Molter, Ursula Maria
Moure, María del Carmen
Quintero, Alejandro Daniel
author Molter, Ursula Maria
author_facet Molter, Ursula Maria
Moure, María del Carmen
Quintero, Alejandro Daniel
author_role author
author2 Moure, María del Carmen
Quintero, Alejandro Daniel
author2_role author
author
dc.subject.none.fl_str_mv CRYSTAL GROUPS
APPROXIMATION PROPERTY
COMPOSITE DILATIONS
REFINEMENT EQUATION
ACCURACY
topic CRYSTAL GROUPS
APPROXIMATION PROPERTY
COMPOSITE DILATIONS
REFINEMENT EQUATION
ACCURACY
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 Γ be a crystal group in Rd. A function φ:Rd⟶C is said to be crystal-refinable (or Γ-refinable) if it is a linear combination of finitely many of the rescaled and translated functions φ(γ−1(ax)), where the translationsγ are taken on a crystal group Γ, and a is an expansive dilation matrix such that aΓa−1⊂Γ. A Γ-refinable function φ:Rd→C satisfies a refinement equation φ(x)=∑γ∈Γdγφ(γ−1(ax)) with dγ∈C. Let S(φ) be the linear span of {φ(γ−1(x)):γ∈Γ} and Sh={f(x/h):f∈S(φ)}. One important property of S(φ) is, how well it approximates functions in L2(Rd). This property is very closely related to the crystal-accuracy of S(φ), which is the highest degree p such that all multivariate polynomials q(x) of degree(q)
Fil: Molter, Ursula Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Moure, María del Carmen. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Quintero, Alejandro Daniel. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Let Γ be a crystal group in Rd. A function φ:Rd⟶C is said to be crystal-refinable (or Γ-refinable) if it is a linear combination of finitely many of the rescaled and translated functions φ(γ−1(ax)), where the translationsγ are taken on a crystal group Γ, and a is an expansive dilation matrix such that aΓa−1⊂Γ. A Γ-refinable function φ:Rd→C satisfies a refinement equation φ(x)=∑γ∈Γdγφ(γ−1(ax)) with dγ∈C. Let S(φ) be the linear span of {φ(γ−1(x)):γ∈Γ} and Sh={f(x/h):f∈S(φ)}. One important property of S(φ) is, how well it approximates functions in L2(Rd). This property is very closely related to the crystal-accuracy of S(φ), which is the highest degree p such that all multivariate polynomials q(x) of degree(q)
publishDate 2019
dc.date.none.fl_str_mv 2019-10-24
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/11336/136210
Molter, Ursula Maria; Moure, María del Carmen; Quintero, Alejandro Daniel; Approximation by crystal-refinable functions; Springer; Geometriae Dedicata; 207; 1; 24-10-2019; 1-21
0046-5755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136210
identifier_str_mv Molter, Ursula Maria; Moure, María del Carmen; Quintero, Alejandro Daniel; Approximation by crystal-refinable functions; Springer; Geometriae Dedicata; 207; 1; 24-10-2019; 1-21
0046-5755
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://link.springer.com/article/10.1007%2Fs10711-019-00483-9
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-019-00483-9
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1701.08226
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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