FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 4, PAGES 1059-1068

On the works of S. B. Stechkin on approximation of periodic functions by polynomials

S. A. Telyakovskii

Abstract

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We give a survey of S. B. Stechkin's works devoted to the following themes: direct and inverse theorems in the theory of best approximations; finding the order of decreasing of Kolmogorov's width for classes of differentiable functions; approximative properties of partial sums of Fourier and Taylor series as well as that of the Fej\`er and Valle\'e Poussin sums; the criterion of absolute convergence for Fourier series in terms of $n$-term approximation.

All articles are published in Russian.

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