Geodesic
Extension of the lower Telyakovskii estimate for the sum of a sine-series with convex coefficient sequence to a longer segment
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 26-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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The lower estimate of the sum of a sine series with a convex sequence of coefficients obtained by S. A. Telyakovskiĭ is extended to a much longer segment. 
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A. Yu. Popov; A. P. Solodov. Extension of the lower Telyakovskii estimate for the sum of a sine-series with convex coefficient sequence to a longer segment. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 26-32. http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a3/

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[2] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965

[3] Salem R., “Détermination de l'ordre de grandeur á l'origine de certaines séries trigonométriques”, C. R. Acad. Sci. Paris, 186 (1928), 1804–1806

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[5] Telyakovskiĭ S.A., “On the behavior near the origin of the sine series with convex coefficients”, Publ. Inst. Math. (Beograd), 58(72) (1995), 43–50 | MR | Zbl

[6] Solodov A.P., “Tochnye konstanty v dvustoronnei otsenke S.A. Telyakovskogo summy ryada po sinusam s vypukloi posledovatelnostyu koeffitsientov”, Matem. zametki, 107:6 (2020), 906–921 | DOI | Zbl

[7] Popov A.Yu., Solodov A.P., “Optimalnye na otrezke $[\pi/2,\pi]$ dvustoronnie otsenki summy sinus-ryada s vypukloi posledovatelnostyu koeffitsientov”, Matem. zametki, 112:2 (2022), 317–320 | DOI

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