Abstract
In this paper, we obtain sufficient conditions for the uniform convergence of trigonometric series with monotone (in the extended sense) coefficients.
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References
S. A. Telyakovskii, “On the uniform convergence of trigonometric series with rarely changing coefficients,” Mat. Zametki [Math. Notes] 70(4), 613–620 (2001).
A. S. Belov, “Remarks on mean convergence (and boundedness) of partial sums of trigonometric series,” Mat. Zametki [Math. Notes] 71(6), 807–817 (2002).
L. Leindler, “Integrability of sine and cosine having coefficients of a new class,” Austrian J. Math. Anal. Appl. 1(1), Article 4 (2004).
S. B. Stechkin, “Trigonometric series with monotone type coefficients,” in Approximation Theory: Asymptotical Expansions. Suppl. 1, Proc. Steklov Inst. Math. (MAIK-Nauka, Moscow, 2001), pp. 214–224.
S. A. Telyakovskii, “Some properties of Fourier series of functions with bounded variation,” East J. Approx. 10(1–2), 215–218 (2004).
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Original Russian Text © S. Yu. Tikhonov, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 2, pp. 304–310.
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Tikhonov, S.Y. On the uniform convergence of trigonometric series. Math Notes 81, 268–274 (2007). https://doi.org/10.1134/S0001434607010294
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DOI: https://doi.org/10.1134/S0001434607010294