Extra invariance of shift-invariant spaces on LCA groups

• Autores: Anastasio, M.; Cabrelli, C.; Paternostro, V.
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Math. Anal. Appl. 2010;370(2):530-537
• Materia: Fiber spaces; LCA groups; Range functions; Shift-invariant space; Translation invariant space
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.
Fil:Anastasio, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.