Shift-invariant spaces on LCA groups |
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Authors: | Carlos Cabrelli Victoria Paternostro |
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Institution: | a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina b CONICET, Argentina |
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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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Keywords: | Shift-invariant spaces Translation invariant spaces LCA groups Range functions Fibers |
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