TY - JOUR AU - V. F. Babenko AU - T. Yu. Leskevich PY - 2012/08/25 Y2 - 2024/03/28 TI - Approximation of some classes of functions of many variables by harmonic splines JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 8 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2636 AB - 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 $L_{1}(\Omega)$. ER -