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

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.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-04, Vol.340 (1), p.219-225
Main Authors: Kamyabi Gol, R.A., Tousi, R. Raisi
Format: Article
Language:English
Subjects:
Exact sciences and technology
Geometry
Group theory
Group theory and generalizations
Locally compact abelian group
Mathematical analysis
Mathematics
Operator theory
Parseval frame
Principle shift invariant space
Sciences and techniques of general use
Shift invariant space
Topological groups, lie groups
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Description
Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.08.039