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Abstract:

This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M' containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance. © 2010 Elsevier Inc.

Registro:

Documento: Artículo
Título:Extra invariance of shift-invariant spaces on LCA groups
Autor:Anastasio, M.; Cabrelli, C.; Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:Fiber spaces; LCA groups; Range functions; Shift-invariant space; Translation invariant space
Año:2010
Volumen:370
Número:2
Página de inicio:530
Página de fin:537
DOI: http://dx.doi.org/10.1016/j.jmaa.2010.05.040
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v370_n2_p530_Anastasio.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v370_n2_p530_Anastasio

Referencias:

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  • Anastasio, M., Cabrelli, C., Paternostro, V., Invariance of a shift-invariant space in several variables (2010) Complex Anal. Oper. Theory
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  • Cabrelli, C., Paternostro, V., Shift-invariant spaces on LCA groups (2010) J. Funct. Anal., 258 (6), pp. 2034-2059
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Citas:

---------- APA ----------
Anastasio, M., Cabrelli, C. & Paternostro, V. (2010) . Extra invariance of shift-invariant spaces on LCA groups. Journal of Mathematical Analysis and Applications, 370(2), 530-537.
http://dx.doi.org/10.1016/j.jmaa.2010.05.040
---------- CHICAGO ----------
Anastasio, M., Cabrelli, C., Paternostro, V. "Extra invariance of shift-invariant spaces on LCA groups" . Journal of Mathematical Analysis and Applications 370, no. 2 (2010) : 530-537.
http://dx.doi.org/10.1016/j.jmaa.2010.05.040
---------- MLA ----------
Anastasio, M., Cabrelli, C., Paternostro, V. "Extra invariance of shift-invariant spaces on LCA groups" . Journal of Mathematical Analysis and Applications, vol. 370, no. 2, 2010, pp. 530-537.
http://dx.doi.org/10.1016/j.jmaa.2010.05.040
---------- VANCOUVER ----------
Anastasio, M., Cabrelli, C., Paternostro, V. Extra invariance of shift-invariant spaces on LCA groups. J. Math. Anal. Appl. 2010;370(2):530-537.
http://dx.doi.org/10.1016/j.jmaa.2010.05.040