The approximation of periodical functions of many variables with high smoothness by rectangular Fourier sums
type: Item
instance of: scholarly article
zbMATH Open document ID: 1250.42015
author: O. A. Novikov
author: V. E. Velichko
author: O. G. Rovenskaya
author: V. I. Bodraya
author: V. I. Rukasov
publication date: 2012-07-31T00:00:00Z
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 6062168
MaRDI profile type: Publication
title: The approximation of periodical functions of many variables with high smoothness by rectangular Fourier sums
published in: Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki
review text: 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.
reviewed by: Evgeny Sevost'yanov
description: scientific article; zbMATH DE number 6062168