Dual finite frames for vector spaces over an arbitrary field with applications

Autores
Morillas, Patricia Mariela
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present paper, we study frames for finitedimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
DUAL FRAMES
FIELDS
HILBERT SPACES
METRIC VECTOR SPACES
ULTRAMETRIC NORMED VECTOR SPACES
VECTOR SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/182868
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/182868
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Dual finite frames for vector spaces over an arbitrary field with applicationsMorillas, Patricia MarielaDUAL FRAMESFIELDSHILBERT SPACESMETRIC VECTOR SPACESULTRAMETRIC NORMED VECTOR SPACESVECTOR SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the present paper, we study frames for finitedimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaNational Academy of Sciences2021-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/182868Morillas, Patricia Mariela; Dual finite frames for vector spaces over an arbitrary field with applications; National Academy of Sciences; Armenian Journal of Mathematics; 13; 2; 5-2021; 1-361829-1163CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://armjmath.sci.am/index.php/ajm/article/view/479info:eu-repo/semantics/altIdentifier/doi/10.52737/18291163-2021.13.2-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:26:07Zoai:ri.conicet.gov.ar:11336/182868instacron: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 11:26:08.123CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Dual finite frames for vector spaces over an arbitrary field with applications
title Dual finite frames for vector spaces over an arbitrary field with applications
spellingShingle Dual finite frames for vector spaces over an arbitrary field with applications
Morillas, Patricia Mariela
DUAL FRAMES
FIELDS
HILBERT SPACES
METRIC VECTOR SPACES
ULTRAMETRIC NORMED VECTOR SPACES
VECTOR SPACES
title_short Dual finite frames for vector spaces over an arbitrary field with applications
title_full Dual finite frames for vector spaces over an arbitrary field with applications
title_fullStr Dual finite frames for vector spaces over an arbitrary field with applications
title_full_unstemmed Dual finite frames for vector spaces over an arbitrary field with applications
title_sort Dual finite frames for vector spaces over an arbitrary field with applications
dc.creator.none.fl_str_mv Morillas, Patricia Mariela
author Morillas, Patricia Mariela
author_facet Morillas, Patricia Mariela
author_role author
dc.subject.none.fl_str_mv DUAL FRAMES
FIELDS
HILBERT SPACES
METRIC VECTOR SPACES
ULTRAMETRIC NORMED VECTOR SPACES
VECTOR SPACES
topic DUAL FRAMES
FIELDS
HILBERT SPACES
METRIC VECTOR SPACES
ULTRAMETRIC NORMED VECTOR SPACES
VECTOR SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present paper, we study frames for finitedimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description In the present paper, we study frames for finitedimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.
publishDate 2021
dc.date.none.fl_str_mv 2021-05
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/11336/182868
Morillas, Patricia Mariela; Dual finite frames for vector spaces over an arbitrary field with applications; National Academy of Sciences; Armenian Journal of Mathematics; 13; 2; 5-2021; 1-36
1829-1163
CONICET Digital
CONICET
url http://hdl.handle.net/11336/182868
identifier_str_mv Morillas, Patricia Mariela; Dual finite frames for vector spaces over an arbitrary field with applications; National Academy of Sciences; Armenian Journal of Mathematics; 13; 2; 5-2021; 1-36
1829-1163
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://armjmath.sci.am/index.php/ajm/article/view/479
info:eu-repo/semantics/altIdentifier/doi/10.52737/18291163-2021.13.2-1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv National Academy of Sciences
publisher.none.fl_str_mv National Academy of Sciences
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_ 1846781817153126400
score 12.982451

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