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
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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
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Palabras clave: | Frames; LCA groups; Shift-invariant spaces; Zak transform |
Año: | 2015
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Volumen: | 269
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Número: | 5
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Página de inicio: | 1327
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Página de fin: | 1358
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DOI: |
http://dx.doi.org/10.1016/j.jfa.2015.06.009 |
Título revista: | Journal of Functional Analysis
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Título revista abreviado: | J. Funct. Anal.
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ISSN: | 00221236
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CODEN: | JFUAA
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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