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.
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Translated from Problemy Matematicheskogo Analiza 107, 2020, pp. 23-37.
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Dem’yanovich, Y.K. Adaptive Haar Type Wavelets on Manifolds. J Math Sci 251, 797–813 (2020). https://doi.org/10.1007/s10958-020-05130-3
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DOI: https://doi.org/10.1007/s10958-020-05130-3