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arXiv · 1210.7996

Approximation of functions of several variables by linear methods in the space $S^p$

Viktor V. Savchuk·Andriy L. Shidlich
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Abstract

In the spaces $S^p$ of functions of several variables, $2π$-periodic in each variable, we study the approximative properties of operators $A^\vartriangle_{\varrho,r}$ and $P^\vartriangle_{\varrho,s}$, which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes $S^pH_ω$.

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Viktor V. Savchuk, Andriy L. Shidlich. 2012-10-30. Approximation of functions of several variables by linear methods in the space $S^p$. https://doi.org/10.14232/actasm-012-837-8

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