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arXiv · 0905.2373

Shift Invariant Spaces on LCA Groups

Carlos Cabrelli·Victoria Paternostro
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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 .

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Carlos Cabrelli, Victoria Paternostro. 2009-11-17. Shift Invariant Spaces on LCA Groups. https://arxiv.org/abs/0905.2373

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