Direct limits, multiresolution analyses, and wavelets
| Autor: | Lawrence W. Baggett, Arlan Ramsay, Nadia S. Larsen, Iain Raeburn, Judith A. Packer |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Direct limit Multiresolution analysis 01 natural sciences Dilation (operator theory) symbols.namesake Wavelet 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Multiresolution 47D03 Mathematics Sequence Mathematics::Operator Algebras 010102 general mathematics Hilbert space 42C40 Linear subspace Functional Analysis (math.FA) Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs symbols Universal property 010307 mathematical physics Analysis |
| Zdroj: | Journal of Functional Analysis. 258:2714-2738 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2009.08.011 |
| Popis: | A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert spaces which have multiresolution analyses with desired properties. In this paper, we use direct limits, and in particular the universal property which characterizes them, to construct wavelet bases in a variety of concrete Hilbert spaces of functions. Our results apply to the classical situation involving dilation matrices on $L^2(\R^n)$, the wavelets on fractals studied by Dutkay and Jorgensen, and Hilbert spaces of functions on solenoids. Comment: 23 pages including bibligraphy |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect