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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/182868
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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 Técnicas2025-09-29T09:56:54Zoai: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:34982025-09-29 09:56:54.946CONICET 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 |
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1844613706096312320 |
score |
13.070432 |