Embedding of spaces and wavelet decomposition

Dem′yanovich, Yu.

doi:10.1090/spmj/1607

Embedding of spaces and wavelet decomposition
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by Yu. K. Dem′yanovich
Translated by: the author

St. Petersburg Math. J. 31 (2020), 435-453

DOI: https://doi.org/10.1090/spmj/1607

Published electronically: April 30, 2020

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Abstract:

Necessary and sufficient conditions of generalized smoothness (called pseudosmoothness) are found for coordinate functions of the finite element method (FEM). Embedding of FEM spaces on embedded subdivisions is discussed. Approximation relations on a differentiable manifold are considered. The concept of pseudosmoothness is formulated in terms of the coincidence of values for linear functionals on functions in question. The concept of maximum pseudosmoothness is introduced. Embedding criteria for spaces on embedded subdivisions are given. Wavelet expansion algorithms are developed for the spaces mentioned above.

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