Approximation by Fourier sums in classes of Weyl--Nagy differentiable functions with high exponent of smoothness

Abstract

We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order $n-1$ of classes of $2\pi$-periodic Weyl--Nagy differentiable functions, $W_{\beta ,p}^r,1\le p\le \infty ,\beta \in \mathbb{R},$ for high exponents of smoothness $r(r-1\ge \sqrt{n})$. We obtain similar estimates in metrics of the spaces $L_p,1\le p\le \infty ,$ for functional classes $W_{\beta ,1}^r$.

16 pages, in Russian language