Shift Invariant Spaces on LCA Groups
Classical Analysis and ODEs
2009-11-17 v3
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 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 .
Keywords
Cite
@article{arxiv.0905.2373,
title = {Shift Invariant Spaces on LCA Groups},
author = {Carlos Cabrelli and Victoria Paternostro},
journal= {arXiv preprint arXiv:0905.2373},
year = {2009}
}
Comments
23 pages. Some small corrections were added. To appear in "Journal of Functional Analysis"