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Article

Keywords:
rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means
Summary:
For real functions of bounded variation in the Hardy sense, $2\pi$-periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.
References:
[1] R. Bojanić: An estimate of the rate of convergence for Fourier series of functions of bounded variation. Publications de L'Institut Mathématique, Nouvelle série 26(40) (1979), 57-60. MR 0572330
[2] C. K. Chui A. S. B. Holland: On the order of approximation by Euler and Taylor means. Journal of Approximation Theory 39 (1983), 24-38. DOI 10.1016/0021-9045(83)90066-7 | MR 0713359
[3] G. H. Hardy: Divergent series. Oxford, 1949. MR 0030620 | Zbl 0032.05801
[4] J. Marcinkiewicz: On a class of functions and their Fourier series. Collected papers. PWN, Warszawa, 1964, pp. 36-41.
[5] R. Taberski: On double integrals and Fourier series. Annales Polon. Math. 15 (1964), 97-115. MR 0167787 | Zbl 0171.30002
[6] L. Tonelli: Série Trigonometrische. Bologna, 1928.
[7] M. Topolewska: On the degree of convergence of Borel and Euler means of trigonometric series. Časopis pro pěstování matematiky 112(3) (1987), 225-232. MR 0905967 | Zbl 0625.42004
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