Global Symmetric Approximation of Frames
- Autores
- Chiumiento, Eduardo Hernán
- Año de publicación
- 2018
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.
Centro de Investigación de Matemática - Materia
-
Matemática
Symmetric approximation
Frame
Hilbert space
Hilbert–Schmidt operator
Index of a pair of projections
Partial isometry
Löwdin orthogonalization - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/123376
Ver los metadatos del registro completo
| id |
SEDICI_a306f2741450ac48402d2238dfad2d2c |
|---|---|
| oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/123376 |
| network_acronym_str |
SEDICI |
| repository_id_str |
1329 |
| network_name_str |
SEDICI (UNLP) |
| spelling |
Global Symmetric Approximation of FramesChiumiento, Eduardo HernánMatemáticaSymmetric approximationFrameHilbert spaceHilbert–Schmidt operatorIndex of a pair of projectionsPartial isometryLöwdin orthogonalizationWe solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components.Centro de Investigación de Matemática2018-07-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1395-1423http://sedici.unlp.edu.ar/handle/10915/123376enginfo:eu-repo/semantics/altIdentifier/issn/1069-5869info:eu-repo/semantics/altIdentifier/issn/1531-5851info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-018-9632-4info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:29:24Zoai:sedici.unlp.edu.ar:10915/123376Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:29:24.772SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Global Symmetric Approximation of Frames |
| title |
Global Symmetric Approximation of Frames |
| spellingShingle |
Global Symmetric Approximation of Frames Chiumiento, Eduardo Hernán Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization |
| title_short |
Global Symmetric Approximation of Frames |
| title_full |
Global Symmetric Approximation of Frames |
| title_fullStr |
Global Symmetric Approximation of Frames |
| title_full_unstemmed |
Global Symmetric Approximation of Frames |
| title_sort |
Global Symmetric Approximation of Frames |
| dc.creator.none.fl_str_mv |
Chiumiento, Eduardo Hernán |
| author |
Chiumiento, Eduardo Hernán |
| author_facet |
Chiumiento, Eduardo Hernán |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization |
| topic |
Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization |
| dc.description.none.fl_txt_mv |
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components. Centro de Investigación de Matemática |
| description |
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components. |
| publishDate |
2018 |
| dc.date.none.fl_str_mv |
2018-07-26 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo 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://sedici.unlp.edu.ar/handle/10915/123376 |
| url |
http://sedici.unlp.edu.ar/handle/10915/123376 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/issn/1069-5869 info:eu-repo/semantics/altIdentifier/issn/1531-5851 info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-018-9632-4 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
| dc.format.none.fl_str_mv |
application/pdf 1395-1423 |
| dc.source.none.fl_str_mv |
reponame:SEDICI (UNLP) instname:Universidad Nacional de La Plata instacron:UNLP |
| reponame_str |
SEDICI (UNLP) |
| collection |
SEDICI (UNLP) |
| instname_str |
Universidad Nacional de La Plata |
| instacron_str |
UNLP |
| institution |
UNLP |
| repository.name.fl_str_mv |
SEDICI (UNLP) - Universidad Nacional de La Plata |
| repository.mail.fl_str_mv |
alira@sedici.unlp.edu.ar |
| _version_ |
1844616172997181440 |
| score |
13.070432 |