Adaptive Haar Type Wavelets on Manifolds

We consider embedded Haar type spaces associated with cell subdivisions of a smooth manifold. We use an adaptivity criterion connected with a nonnegative set function possessing certain monotonicity properties. We propose an algorithm for constructing embedded spaces satisfying the adaptivity criter...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-12, Vol.251 (6), p.797-813
Main Author: Dem’yanovich, Yu. K.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider embedded Haar type spaces associated with cell subdivisions of a smooth manifold. We use an adaptivity criterion connected with a nonnegative set function possessing certain monotonicity properties. We propose an algorithm for constructing embedded spaces satisfying the adaptivity criterion. To construct the wavelet decomposition, we apply the nonclassical approach and obtain the adaptive wavelet decomposition of the Haar type space on the manifold. Some model examples are given.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05130-3