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 
@article{MZM_2008_84_5_a10,
     author = {A. V. Pokrovskii},
     title = {On the {Best} {Approximation} by {Trigonometric} {Polynomials} on {Convolution} {Classes} of {Analytic} {Periodic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {755--762},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a10/}
}
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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/