The approximation of periodical functions of many variables with high smoothness by rectangular Fourier sums
Asymptotical equalities for distortions of rectangular Fourier sums on classes of \(\overline{\psi}\)--integrals of functions of many variables are established. Let \(\tau_{k_i,j}^{(n_i)}\) and \(T_{k_i,j}^{(n_i)},\) \(i,j\in {\mathbb N},\) be two systems of numbers satisfying some conditions. Then we have some relation for \(\delta_{\vec{n}}(f,\vec{x},\Lambda)=f(\vec{x})-U_{\vec{n}}(f,x,\Lambda)\) for every function \(f\in C_{\infty}^{m\overline{\psi}}\) at every point \(\vec{x}\in T^m,\) where \(U_{\vec{n}}(f,x,\Lambda)\) is some polynomial.
scientific article; zbMATH DE number 6062168