Shift-invariant spaces on LCA groups

Abstract

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 anLCA 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 andRiesz bases of these spaces extending previous results, that were known for R^d and the lattice Z^d.