On the Best Approximation by Trigonometric Polynomials on Convolution Classes of Analytic Periodic Functions

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: For a continuous $2\pi$-periodic real-valued function $K(t)$, whose amplitudes decrease as a geometric progression with a denominator $q\in(0,1)$ starting from a given number $n\in\mathbb{N}$, we find sharp upper bounds for $q$ ensuring that $K(t)$ satisfies the Nagy condition $N_n^*$.

Keywords: best approximation, $2\pi$-periodic analytic function, convolution class, trigonometric polynomial, geometric progression, Nagy condition.

UDC: 517.51

Received: 22.05.2007

DOI: 10.4213/mzm6359

 English version: Mathematical Notes, 2008, 84:5, 703–709

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