Approximation of functions of several variables by linear methods in the space $S^p$

Abstract

In the spaces $S^p$ of functions of several variables, $2\pi$-periodic in each variable, we study the approximative properties of operators $A_{\varrho ,r}^{△}$ and $P_{\varrho ,s}^{△}$, which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes $S^p{H}_{\omega }$.

11 pages

Cited by in corpus (3)

• Approximation on hexagonal domains by Taylor-Abel-Poisson means
• Approximation theorems for multivariate Taylor-Abel-Poisson means
• Actual problems of the approximation theory in metrics of discrete spaces on sets of summable periodic and almost periodic functions