Geodesic
On the Best Approximation by Trigonometric Polynomials on Convolution Classes of Analytic Periodic Functions
Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 755-762.

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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, trigonometric polynomial, geometric progression, Nagy condition.
Mots-clés : convolution class 
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A. V. Pokrovskii. On the Best Approximation by Trigonometric Polynomials on Convolution Classes of Analytic Periodic Functions. Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 755-762. http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a10/

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