Geodesic
Uniform-convergence factors for Fourier series of functions with a~given modulus of continuity
Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 33-40.

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It is proved that a sequence of factors $\{\lambda_\nu\}$, which are Fourier–Stieitjes coefficients, converts the Fourier series of any function whose modulus of continuity does not exceed a given modulus of continuity $\omega(\delta)$ into a uniformly convergent series, if and only if $\omega(1/n)\int_o^{2\pi}\left|\lambda_0/2+\sum_{\nu=1}^n\lambda_\nu\cos\nu t\right|dt=o(1)$. The sufficiency of this condition is known. 
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     author = {S. A. Telyakovskii},
     title = {Uniform-convergence factors for {Fourier} series of functions with a~given modulus of continuity},
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     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/}
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S. A. Telyakovskii. Uniform-convergence factors for Fourier series of functions with a~given modulus of continuity. Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 33-40. http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/