Shift Invariant Spaces on LCA Groups

Details Shift Invariant Spaces on LCA Groups Shift Invariant Spaces on LCA Groups

2009-05-14

arxiv.org/abs/0905.2373v3

Mathematics

Classical Analysis and ODEs

23 pages. Some small corrections were added. To appear in "Journal of Functional Analysis"

Scientific paper

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 Rd and the lattice Zd .

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