Geodesic
Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients
Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 865-874

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The paper examines the following question: Under what orders of monotonicity are the upper and lower bounds of the sum of a cosine series near zero valid if they are obtained using the function $\sum_{n=0}^{[\pi/x]}(n+1)\Delta(\mathbf a)_n$?
Keywords: Fourier series, asymptotics
Mots-clés : monotone coefficients. 
@article{MZM_2021_110_6_a4,
     author = {M. I. Dyachenko},
     title = {Asymptotics of {Sums} of {Cosine} {Series} with {Fractional} {Monotonicity} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {865--874},
     publisher = {mathdoc},
     volume = {110},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a4/}
}
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M. I. Dyachenko. Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients. Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 865-874. http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a4/