2017
Том 69
№ 9

All Issues

Approximation of some classes of functions of many variables by harmonic splines

Babenko V. F., Leskevich T. Yu.

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Abstract

We determine the exact values of upper bounds of the error of approximation by harmonic splines for functions $u$ defined on an $n$-dimensional parallelepiped $\Omega$ forwhich $||\Delta u||_{L_{\infty}(\Omega)} \leq 1$ and for functions $u$ defined on $\Omega$ forwhich $||\Delta u||_{L_{p}(\Omega)} \leq 1, \quad 1 \leq p \leq \infty$. In the first case, the error is estimated in $L_{p}(\Omega), \quad 1 \leq p \leq \infty$; in the second case, it is estimated in $L_{1}(\Omega)$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 8, pp 1151-1167.

Citation Example: Babenko V. F., Leskevich T. Yu. Approximation of some classes of functions of many variables by harmonic splines // Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1011-1024.

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