Literature cited
E. P. Dolzhenko, “Behavior of the Fourier series of a continuous function as a function of the rate of its approximation by rational functions (algebraic or trigonometric),” Matem. Sb.,71, No. 1, 43–47 (1966).
R. Salem, “Essais sur les séries trigonométriques,” Actual Sci. et Industr. (Paris), No. 862 (1940).
E. P. Dolzhenko, “Uniform approximation by rational functions (algebraic and trigonometric) and global functional properties,” Dokl. Akad. Nauk SSSR,166, No. 3, 526–529 (1966).
E. A. Sevast'yanov, “Piecewise-monotonic approximation andΦ-variation,” Analysis Mathematica,1, No. 2, 141–164 (1975).
Z. A. Chanturiya, “Modulus of variation of a function and its application to Fourier-series theory,” Dokl. Akad. Nauk SSSR,214, No. 1, 63–66 (1974).
K. I. Oskolkov, “Generalized variation, Banach index, and uniform convergence of Fourier series,” Matem. Zametki,12, No. 3, 313–324 (1972).
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Translated from Matematicheskie Zametki, Vol. 20, No. 4, pp. 619–624, October, 1976.
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Sevast'yanov, E.A. Piecewise-monotonic and rational approximations and uniform convergence of Fourier series. Mathematical Notes of the Academy of Sciences of the USSR 20, 904–907 (1976). https://doi.org/10.1007/BF01098912
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DOI: https://doi.org/10.1007/BF01098912