On approximation properties of matrix-valued multi-resolution analyses
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http://hdl.handle.net/10045/125302
Title: | On approximation properties of matrix-valued multi-resolution analyses |
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Authors: | Dubon, Eric | San Antolín Gil, Ángel |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Approximate continuity | Approximation and density order | Fourier transform | Matrix-valued multi-resolution analysis | Scaling functions |
Knowledge Area: | Álgebra | Análisis Matemático |
Issue Date: | 8-Jul-2022 |
Publisher: | Taylor & Francis |
Citation: | Linear and Multilinear Algebra. 2023, 71(14): 2263-2281. https://doi.org/10.1080/03081087.2022.2095327 |
Abstract: | We study approximation properties of multi-resolution analyses in the context of matrix-valued function spaces. Here, we generalize the notions of approximation order and density order given by the reference [de Boor C, DeVore RA, Ron A. Approximation from shift-invariant subspaces of L2(Rd). Trans Am Math Soc. 1994;341(2):787–806]. Indeed, we prove a characterization of the closed subspaces generated by the shifts of a single matrix-valued function that provide approximation order and/or density order α≥0. To give our conditions, we need the classical notion of approximate continuity. As a consequence, we prove necessary and sufficient conditions on a matrix-valued function to be a scaling function in a multi-resolution analysis. |
URI: | http://hdl.handle.net/10045/125302 |
ISSN: | 0308-1087 (Print) | 1563-5139 (Online) |
DOI: | 10.1080/03081087.2022.2095327 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2022 Informa UK Limited, trading as Taylor & Francis Group |
Peer Review: | si |
Publisher version: | https://doi.org/10.1080/03081087.2022.2095327 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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Dubon_San-Antolin_2022_LinearMultilinearAlgebra_final.pdf | Versión final (acceso restringido) | 1,65 MB | Adobe PDF | Open Request a copy |
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