Sampling Formulae and Optimal Factorizations of Projections

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 sampl...

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Detalles Bibliográficos
Autores principales: Andruchow, Esteban, Antezana, Jorge Abel, Corach, Gustavo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
Sampling
Projections
Frames
Generalized inverses
Shift invarian
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/142790
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-142790
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Sampling
Projections
Frames
Generalized inverses
Shift invarian
spellingShingle Matemática
Sampling
Projections
Frames
Generalized inverses
Shift invarian
Andruchow, Esteban
Antezana, Jorge Abel
Corach, Gustavo
Sampling Formulae and Optimal Factorizations of Projections
topic_facet Matemática
Sampling
Projections
Frames
Generalized inverses
Shift invarian
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.
format Articulo
Articulo
author Andruchow, Esteban
Antezana, Jorge Abel
Corach, Gustavo
author_facet Andruchow, Esteban
Antezana, Jorge Abel
Corach, Gustavo
author_sort Andruchow, Esteban
title Sampling Formulae and Optimal Factorizations of Projections
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
publishDate 2008
url http://sedici.unlp.edu.ar/handle/10915/142790
work_keys_str_mv AT andruchowesteban samplingformulaeandoptimalfactorizationsofprojections
AT antezanajorgeabel samplingformulaeandoptimalfactorizationsofprojections
AT corachgustavo samplingformulaeandoptimalfactorizationsofprojections
bdutipo_str Repositorios
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