Shift-invariant spaces on LCA groups

被引：80

作者：

Cabrelli, Carlos ^{[1
,2
]}

Paternostro, Victoria ^{[1
,2
]}

机构：

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

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 06期

关键词：

Shift-invariant spaces; Translation invariant spaces; LCA groups; Range functions; Fibers; SUBSPACES; L(2)(R(D));

D O I：

10.1016/j.jfa.2009.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for R(d) and the lattice Z(d). (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2034 / 2059

页数：26

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