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Classification of Generalized Multiresolution Analyses | | Lawrence W. Baggett
; Veronika Furst
; Kathy D. Merrill
; Judith A. Packer
; | | Date: |
28 Oct 2009 | | 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. | | Source: | arXiv, 0910.5446 | | Services: | Forum | Review | PDF | Favorites | |
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