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Abstract:

We study closed subspaces of L2(X), where (X,μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X. We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of frames and Riesz sequences in L2(X) generated by the action of the unitary representation under consideration on a countable set of functions in L2(X). Finally, closed subspaces of L2(G), for G being an LCA group, that are invariant under translations by elements on a closed subgroup Γ of G are studied and characterized. The results we obtain for this case are applicable to cases where those already proven in [5,7] are not. © 2015 Elsevier Inc.

Registro:

Documento: Artículo
Título:The Zak transform and the structure of spaces invariant by the action of an LCA group
Autor:Barbieri, D.; Hernández, E.; Paternostro, V.
Filiación:Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28049, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:Frames; LCA groups; Shift-invariant spaces; Zak transform
Año:2015
Volumen:269
Número:5
Página de inicio:1327
Página de fin:1358
DOI: http://dx.doi.org/10.1016/j.jfa.2015.06.009
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v269_n5_p1327_Barbieri

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Citas:

---------- APA ----------
Barbieri, D., Hernández, E. & Paternostro, V. (2015) . The Zak transform and the structure of spaces invariant by the action of an LCA group. Journal of Functional Analysis, 269(5), 1327-1358.
http://dx.doi.org/10.1016/j.jfa.2015.06.009
---------- CHICAGO ----------
Barbieri, D., Hernández, E., Paternostro, V. "The Zak transform and the structure of spaces invariant by the action of an LCA group" . Journal of Functional Analysis 269, no. 5 (2015) : 1327-1358.
http://dx.doi.org/10.1016/j.jfa.2015.06.009
---------- MLA ----------
Barbieri, D., Hernández, E., Paternostro, V. "The Zak transform and the structure of spaces invariant by the action of an LCA group" . Journal of Functional Analysis, vol. 269, no. 5, 2015, pp. 1327-1358.
http://dx.doi.org/10.1016/j.jfa.2015.06.009
---------- VANCOUVER ----------
Barbieri, D., Hernández, E., Paternostro, V. The Zak transform and the structure of spaces invariant by the action of an LCA group. J. Funct. Anal. 2015;269(5):1327-1358.
http://dx.doi.org/10.1016/j.jfa.2015.06.009