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. 
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     author = {M. I. Dyachenko},
     title = {Asymptotics of {Sums} of {Cosine} {Series} with {Fractional} {Monotonicity} {Coefficients}},
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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/

[1] R. Salem, Essais sur les séries trigonométriques, Hermann et Cie., Paris, 1940 | MR

[2] H. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[3] S. A. Telyakovskii, “K voprosu o povedenii ryadov po sinusam vblizi nulya”, Makedon. Acad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi, 21:1-2 (2000), 47–54 | MR

[4] A. Yu. Popov, A. P. Solodov, “Otsenki s tochnymi konstantami summ nekotorykh klassov ryadov po sinusam s monotonnymi koeffitsientami cherez mazhorantu Salema”, Matem. zametki, 104:5 (2018), 725–736 | DOI | MR

[5] A. Yu. Popov, “Utochnenie otsenok summ sinus-ryadov s monotonnymi i kosinus-ryadov s vypuklymi koeffitsientami”, Matem. zametki, 109:5 (2021), 768–780 | DOI

[6] M. I. Dyachenko, “Trigonometricheskie ryady s obobschenno-monotonnymi koeffitsientami”, Izv. vuzov. Matem., 1986, no. 7, 39–50 | MR | Zbl

[7] A. Zigmund, Trigonometricheskie ryady, T. 1, Mir, M., 1965 | MR | Zbl

[8] A. F. Andersen, “Comparison theorems in the theory of Cesaro summability”, Proc. London Math. Soc. (2), 27:1 (1927), 39–71 | MR