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arXiv · 0910.5446

Classification of Generalized Multiresolution Analyses

Lawrence W. Baggett·Veronika Furst·Kathy D. Merrill·Judith A. Packer
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Abstract

We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions $m$ and matrix-valued filter functions $H$. Given a natural number valued function $m$ and a system of functions encoded in a matrix $H$ satisfying certain conditions, a construction procedure is described that produces an abstract GMRA with multiplicity function $m $ and filter system $H$. An equivalence relation on GMRAs is defined and described in terms of their associated pairs $(m,H)$. This classification system is applied to classical examples in $L^2 (\mathbb R^d)$ as well as to previously studied abstract examples.

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Lawrence W. Baggett, Veronika Furst, Kathy D. Merrill, Judith A. Packer. 2009-10-28. Classification of Generalized Multiresolution Analyses. https://arxiv.org/abs/0910.5446

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