@article{Babenko_Leskevich_2012, title={Approximation of some classes of functions of many variables by harmonic splines}, volume={64}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2636}, abstractNote={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 $L_{1}(\Omega)$.}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Babenko, V. F. and Leskevich, T. Yu.}, year={2012}, month={Aug.}, pages={1011-1024} }