On the Uniform Convergence of Trigonometric Series
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 304-310.

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In this paper, we obtain sufficient conditions for the uniform convergence of trigonometric series with monotone (in the extended sense) coefficients.
Keywords: trigonometric series, monotone (in the extended sense) sequence, lacunary sequence
Mots-clés : uniform convergence, quasimonotone sequence, Abel transformation.
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S. Yu. Tikhonov. On the Uniform Convergence of Trigonometric Series. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 304-310. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a12/

[1] S. A. Telyakovskii, “O ravnomernoi skhodimosti trigonometricheskikh ryadov s redko menyayuschimisya koeffitsientami”, Matem. zametki, 70:4 (2001), 613–620 | MR | Zbl

[2] A. S. Belov, “Zamechaniya o skhodimosti (i ogranichennosti) v srednem chastnykh summ trigonometricheskogo ryada”, Matem. zametki, 71:6 (2002), 807–817 | MR | Zbl

[3] L. Leindler, “Integrability of sine and cosine having coefficients of a new class”, Aust. J. Math. Anal. Appl., 1:1 (2004), Article 4 | MR | Zbl

[4] S. B. Stechkin, “Trigonometric series with monotone type coefficients”, Approximation Theory. Asymptotical Expansions, Proc. Steklov Inst. Math., MAIK-Nauka, Moscow, 2001, S214–S224 | MR | Zbl

[5] S. A. Telyakovskii, “Some properties of Fourier series of functions with bounded variation”, East J. Approx., 10:1–2 (2004), 215–218 | MR | Zbl