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Abstract:

In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd. © 2009 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Shift-invariant spaces on LCA groups
Autor:Cabrelli, C.; Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Fibers; LCA groups; Range functions; Shift-invariant spaces; Translation invariant spaces
Año:2010
Volumen:258
Número:6
Página de inicio:2034
Página de fin:2059
DOI: http://dx.doi.org/10.1016/j.jfa.2009.11.013
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00221236_v258_n6_p2034_Cabrelli.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v258_n6_p2034_Cabrelli

Referencias:

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  • Kamyabi Gol, R.A., Raisi Tousi, R., The structure of shift invariant spaces on a locally compact abelian group (2008) J. Math. Anal. Appl., 340, pp. 219-225
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Citas:

---------- APA ----------
Cabrelli, C. & Paternostro, V. (2010) . Shift-invariant spaces on LCA groups. Journal of Functional Analysis, 258(6), 2034-2059.
http://dx.doi.org/10.1016/j.jfa.2009.11.013
---------- CHICAGO ----------
Cabrelli, C., Paternostro, V. "Shift-invariant spaces on LCA groups" . Journal of Functional Analysis 258, no. 6 (2010) : 2034-2059.
http://dx.doi.org/10.1016/j.jfa.2009.11.013
---------- MLA ----------
Cabrelli, C., Paternostro, V. "Shift-invariant spaces on LCA groups" . Journal of Functional Analysis, vol. 258, no. 6, 2010, pp. 2034-2059.
http://dx.doi.org/10.1016/j.jfa.2009.11.013
---------- VANCOUVER ----------
Cabrelli, C., Paternostro, V. Shift-invariant spaces on LCA groups. J. Funct. Anal. 2010;258(6):2034-2059.
http://dx.doi.org/10.1016/j.jfa.2009.11.013