Extra invariance of shift-invariant spaces on LCA groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:370

Article

Anastasio, Magali^1,2  Cabrelli, Carlos^1,2  Paternostro, Victoria^1,2 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, Consejo Nacl Invest Cient & Tecn, RA-1033 Buenos Aires, DF, Argentina

关键词: Shift-invariant space;    Translation invariant space;    LCA groups;    Range functions;    Fiber spaces;   

DOI  :  10.1016/j.jmaa.2010.05.040

来源: Elsevier

【 摘 要 】

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 L-2(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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free