2009/05/14 by Carlos Cabrelli, Cabrelli, Carlos, Victoria Paternostro +1 · 1 citation
Mathematics · #Mathematical Analysis and Transform Methods #math.CA #msc:43A15 #msc:43A77
paper · pdf · doi:10.48550/arxiv.0905.2373
23 pages. Some small corrections were added. To appear in "Journal of Functional Analysis"
arxiv created 2009/11/17 · arxiv updated 2009/12/01
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 .