Optimal dual frames and frame completions for majorization
- Autores
- Massey, Pedro Gustavo; Ruiz, Mariano Andrés; Stojanoff, Demetrio
- Año de publicación
- 2013
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto-Fickus frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Matemática
Dual frames
Frame completions
Frames
Majorization
Schur-Horn - 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:10915/85460
Ver los metadatos del registro completo
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Optimal dual frames and frame completions for majorizationMassey, Pedro GustavoRuiz, Mariano AndrésStojanoff, DemetrioCiencias ExactasMatemáticaDual framesFrame completionsFramesMajorizationSchur-HornIn this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto-Fickus frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.Facultad de Ciencias Exactas2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf201-223http://sedici.unlp.edu.ar/handle/10915/85460enginfo:eu-repo/semantics/altIdentifier/issn/1063-5203info:eu-repo/semantics/altIdentifier/doi/10.1016/j.acha.2012.03.011info: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:UNLP2025-10-15T11:08:27Zoai:sedici.unlp.edu.ar:10915/85460Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:08:27.368SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Optimal dual frames and frame completions for majorization |
| title |
Optimal dual frames and frame completions for majorization |
| spellingShingle |
Optimal dual frames and frame completions for majorization Massey, Pedro Gustavo Ciencias Exactas Matemática Dual frames Frame completions Frames Majorization Schur-Horn |
| title_short |
Optimal dual frames and frame completions for majorization |
| title_full |
Optimal dual frames and frame completions for majorization |
| title_fullStr |
Optimal dual frames and frame completions for majorization |
| title_full_unstemmed |
Optimal dual frames and frame completions for majorization |
| title_sort |
Optimal dual frames and frame completions for majorization |
| dc.creator.none.fl_str_mv |
Massey, Pedro Gustavo Ruiz, Mariano Andrés Stojanoff, Demetrio |
| author |
Massey, Pedro Gustavo |
| author_facet |
Massey, Pedro Gustavo Ruiz, Mariano Andrés Stojanoff, Demetrio |
| author_role |
author |
| author2 |
Ruiz, Mariano Andrés Stojanoff, Demetrio |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Matemática Dual frames Frame completions Frames Majorization Schur-Horn |
| topic |
Ciencias Exactas Matemática Dual frames Frame completions Frames Majorization Schur-Horn |
| dc.description.none.fl_txt_mv |
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto-Fickus frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above. Facultad de Ciencias Exactas |
| description |
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto-Fickus frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above. |
| publishDate |
2013 |
| dc.date.none.fl_str_mv |
2013 |
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eng |
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