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Mat. Zametki, 2008, Volume 84, Issue 5, Pages 755–762 (Mi mz6359)  

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

DOI: https://doi.org/10.4213/mzm6359

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

Bibliographic databases:

UDC: 517.51
Received: 22.05.2007

Citation: A. V. Pokrovskii, “On the Best Approximation by Trigonometric Polynomials on Convolution Classes of Analytic Periodic Functions”, Mat. Zametki, 84:5 (2008), 755–762; Math. Notes, 84:5 (2008), 703–709

Citation in format AMSBIB
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