Classification of generalized multiresolution analyses
| Autor: | Judith A. Packer, Lawrence W. Baggett, Kathy D. Merrill, Veronika Furst |
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| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Natural number 01 natural sciences Filter system symbols.namesake 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Equivalence relation 0101 mathematics Ruelle operator 47D03 Mathematics Filter 010102 general mathematics Hilbert space Multiplicity (mathematics) 42C40 Functional Analysis (math.FA) Mathematics - Functional Analysis Generalized multiresolution analysis Mathematics - Classical Analysis and ODEs symbols 010307 mathematical physics Wavelet MRAS Analysis |
| Zdroj: | Journal of Functional Analysis. 258(12):4210-4228 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2009.12.001 |
| Popis: | 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. Comment: 18 pages including bibliograph |
| Databáze: | OpenAIRE |
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