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On approximation properties of matrix-valued multi-resolution analyses.
- Source :
-
Linear & Multilinear Algebra . Sep2023, Vol. 71 Issue 14, p2263-2281. 19p. - Publication Year :
- 2023
-
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 L 2 (R d). 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUNCTION spaces
*FOURIER transforms
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 71
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 169973422
- Full Text :
- https://doi.org/10.1080/03081087.2022.2095327