Approximation by Partial Sums of Fourier Series and the Best Approximation of Certain Function Classes

Author: Shvetsova A.M.

Source: Analysis Mathematica, Volume 27, Number 3, 2001 , pp. 201-222(22)

Publisher: Springer

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Abstract:

Continuing investigations of S. A. Telyakovskii, S. B. Stechkin, A. I. Stepanets and R. M. Trigub, the author studies two questions about approximation of the class of periodic functions with a bounded psi -derivative by polynomials in the spaces C and L.

First, the asymptotics of approximation by partial sums of Fourier series has been found without limitations for the decreasing order of psi . Second, the exact decreasing order of the best approximation of the class has been found. New examples are also given.

Language: English

Document Type: Regular paper

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