Sampling Formulae and Optimal Factorizations of Projections
- Autores
- Andruchow, Esteban; Antezana, Jorge Abel; Corach, Gustavo
- Año de publicación
- 2008
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection from H onto W with null space M⊥. We study decompositions like Qf = ∑n∊ℕ 〈 f, hn〉 fn, where {fn}n∊ℕ and {hn}n∊ℕ are frames for the subspaces W and M, respectively. This type of decompositions corresponds to sampling formulae. By considering the synthesis operator F (resp. H) of the sequence {fn}n∊ℕ (resp. {hn}n∊ℕ), the formula above can be expressed as the factorization Q = FH*. We study different properties of these factorizations and decompositions of oblique and orthogonal projections. Several characterizations of these decompositions are presented. By means of an operator inequality for positive operators, we get a result which minimizes the norm of F — H.
Facultad de Ciencias Exactas
Facultad de Ingeniería - Materia
-
Matemática
Sampling
Projections
Frames
Generalized inverses
Shift invarian - 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:10915/142790
Ver los metadatos del registro completo
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Sampling Formulae and Optimal Factorizations of ProjectionsAndruchow, EstebanAntezana, Jorge AbelCorach, GustavoMatemáticaSamplingProjectionsFramesGeneralized inversesShift invarianLet H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection from H onto W with null space M⊥. We study decompositions like Qf = ∑n∊ℕ 〈 f, hn〉 fn, where {fn}n∊ℕ and {hn}n∊ℕ are frames for the subspaces W and M, respectively. This type of decompositions corresponds to sampling formulae. By considering the synthesis operator F (resp. H) of the sequence {fn}n∊ℕ (resp. {hn}n∊ℕ), the formula above can be expressed as the factorization Q = FH*. We study different properties of these factorizations and decompositions of oblique and orthogonal projections. Several characterizations of these decompositions are presented. By means of an operator inequality for positive operators, we get a result which minimizes the norm of F — H.Facultad de Ciencias ExactasFacultad de Ingeniería2008-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf313-331http://sedici.unlp.edu.ar/handle/10915/142790enginfo:eu-repo/semantics/altIdentifier/issn/1530-6429info:eu-repo/semantics/altIdentifier/doi/10.1007/bf03549503info: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:UNLP2025-10-15T11:24:24Zoai:sedici.unlp.edu.ar:10915/142790Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:24:25.096SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Sampling Formulae and Optimal Factorizations of Projections |
| title |
Sampling Formulae and Optimal Factorizations of Projections |
| spellingShingle |
Sampling Formulae and Optimal Factorizations of Projections Andruchow, Esteban Matemática Sampling Projections Frames Generalized inverses Shift invarian |
| title_short |
Sampling Formulae and Optimal Factorizations of Projections |
| title_full |
Sampling Formulae and Optimal Factorizations of Projections |
| title_fullStr |
Sampling Formulae and Optimal Factorizations of Projections |
| title_full_unstemmed |
Sampling Formulae and Optimal Factorizations of Projections |
| title_sort |
Sampling Formulae and Optimal Factorizations of Projections |
| dc.creator.none.fl_str_mv |
Andruchow, Esteban Antezana, Jorge Abel Corach, Gustavo |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban Antezana, Jorge Abel Corach, Gustavo |
| author_role |
author |
| author2 |
Antezana, Jorge Abel Corach, Gustavo |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Matemática Sampling Projections Frames Generalized inverses Shift invarian |
| topic |
Matemática Sampling Projections Frames Generalized inverses Shift invarian |
| dc.description.none.fl_txt_mv |
Let H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection from H onto W with null space M⊥. We study decompositions like Qf = ∑n∊ℕ 〈 f, hn〉 fn, where {fn}n∊ℕ and {hn}n∊ℕ are frames for the subspaces W and M, respectively. This type of decompositions corresponds to sampling formulae. By considering the synthesis operator F (resp. H) of the sequence {fn}n∊ℕ (resp. {hn}n∊ℕ), the formula above can be expressed as the factorization Q = FH*. We study different properties of these factorizations and decompositions of oblique and orthogonal projections. Several characterizations of these decompositions are presented. By means of an operator inequality for positive operators, we get a result which minimizes the norm of F — H. Facultad de Ciencias Exactas Facultad de Ingeniería |
| description |
Let H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection from H onto W with null space M⊥. We study decompositions like Qf = ∑n∊ℕ 〈 f, hn〉 fn, where {fn}n∊ℕ and {hn}n∊ℕ are frames for the subspaces W and M, respectively. This type of decompositions corresponds to sampling formulae. By considering the synthesis operator F (resp. H) of the sequence {fn}n∊ℕ (resp. {hn}n∊ℕ), the formula above can be expressed as the factorization Q = FH*. We study different properties of these factorizations and decompositions of oblique and orthogonal projections. Several characterizations of these decompositions are presented. By means of an operator inequality for positive operators, we get a result which minimizes the norm of F — H. |
| publishDate |
2008 |
| dc.date.none.fl_str_mv |
2008-09-01 |
| 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 |
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article |
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publishedVersion |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/1530-6429 info:eu-repo/semantics/altIdentifier/doi/10.1007/bf03549503 |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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