Embedding of spaces and wavelet decomposition

Research output

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.

Original languageEnglish
Pages (from-to)435-453
Number of pages19
JournalSt. Petersburg Mathematical Journal
Volume31
Issue number3
DOIs
Publication statusPublished - 2020

Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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