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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Embedding of spaces and wavelet decomposition

Author: Yu. K. Dem′yanovich
Translated by: the author
Original publication: Algebra i Analiz, tom 31 (2019), nomer 3.
Journal: St. Petersburg Math. J. 31 (2020), 435-453
MSC (2010): Primary 41A15
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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Additional Information

Yu. K. Dem′yanovich
Affiliation: St. Petersburg State University

Keywords: Approximation relations, generalized smoothness, nesting of spaces, wavelet expansions, minimal splines, finite element method, functions on a manifold
Received by editor(s): December 3, 2018
Published electronically: April 30, 2020
Additional Notes: This work was partially supported by RFBR grant 15-01-008847.
Dedicated: Dedicated to the blessed memory of dear teacher and friend Solomon Grigorievich Mikhlin
Article copyright: © Copyright 2020 American Mathematical Society