Geodesic
Uniform Convergence of Sine Series with Fractional-Monotone Coefficients
Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 339-346

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We study how the well-known criterion for the uniform convergence of a sine series with monotone coefficients changes if, instead of monotonicity, one imposes the condition of $\alpha$-monotonicity with $0\alpha 1$. Moreover, we obtain an addition to the well-known Kolmogorov theorem on the integrability of the sum of a cosine series with convex coefficients tending to zero.
Keywords: trigonometric series, Cesaro numbers.
Mots-clés : uniform convergence 
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     author = {M. I. Dyachenko},
     title = {Uniform {Convergence} of {Sine} {Series} with {Fractional-Monotone} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {339--346},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/}
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M. I. Dyachenko. Uniform Convergence of Sine Series with Fractional-Monotone Coefficients. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 339-346. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/