Abstract
We show that if the module of continuity ω(ƒ, δ) of a 2π-periodic function ƒ ∈ {ie081-01} is o(1/ log log 1/δ) as δ → 0+, then there exists a rearrangement of the trigonometric Fourier series of ƒ converging uniformly to ƒ.
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References
S. A. Chobanian, “The structure of the set of sums of a conditionally convergent series in a normed space,” Dokl Akad. Nauk SSSR, 278, No. 3, 556–559 (1984).
S. A. Chobanian, “The structure of the set of sums of a conditionally convergent series in a normed space,” Mat. Sb., 128, No. 1, 50–65 (1985).
J.-P. Kahane, Random Functional Series [Russian translation], Mir, Moscow (1973).
S. V. Konyagin, “On rearrangements of trigonometric Fourier series,” in All-Union school “Theory of Function Approximations,” Kiev (1989), p. 80.
K. Prachar, Distribution of Prime Numbers, [Russian translation], Mir, Moscow (1967).
S. G. Révész, “Rearrangements of Fourier series,” J. Approx. Theory., 60, No. 1, 101–121 (1990).
S. G. Révész, “On the convergence of Fourier series of U.A.P functions,” J. Math. Anal. Appl., 151, No. 2, 308–317 (1990).
P. L. Ulianov, “Problems on the trigonometric series theory,” Usp. Mat. Nauk, 19, No. 1, 3–69 (1964).
V. V. Zhuk, Approximations of Periodic Functions [in Russian], Leningrad (1982).
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Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.
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Konyagin, S.V. On uniformly convergent rearrangements of trigonometric Fourier series. J Math Sci 155, 81–88 (2008). https://doi.org/10.1007/s10958-008-9209-x
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DOI: https://doi.org/10.1007/s10958-008-9209-x