Generalized low-pass filters and multiresolution analyses

Details Generalized low-pass filters and multiresolution analyses Generalized low-pass filters and multiresolution analyses

2008-12-10

arxiv.org/abs/0812.2042v1

Mathematics

Classical Analysis and ODEs

20 pages including bibliography

Scientific paper

We study generalized filters that are associated to multiplicity functions and homomorphisms of the dual of an abelian group. These notions are based on the structure of generalized multiresolution analyses. We investigate when the Ruelle operator corresponding to such a filter is a pure isometry, and then use that characterization to study the problem of when a collection of closed subspaces, which satisfies all the conditions of a GMRA except the trivial intersection condition, must in fact have a trivial intersection. In this context, we obtain a generalization of a theorem of Bownik and Rzeszotnik.

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