The structure of shift invariant spaces on a locally compact abelian group

摘要

We investigate shift invariant subspaces of L-2(G), where G is a locally compact abelian group. We show, among other things, that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. (c) 2007 Elsevier Inc. All rights reserved.