Approximation by Fourier sums in classes of Weyl – Nagy differentiable functions with high exponent of smoothness
Abstract
UDC 517.5
We establish asymptotic estimates for the least upper bound of approximations in the uniform metric by Fourier sums of order $n-1$ in classes of $2\pi$-periodic Weyl-Nagy differentiable functions $W^r_{\beta,p},$ $1\le p\le \infty,$ $\beta\in\mathbb{R},$ with high exponents of smoothness $r\ (r-1\ge \sqrt{n}).$ We also obtain similar estimates for functional classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty.$
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