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Order of (C,α)-approximations on certain classes of periodic functions

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Abstract

In the spaces L and C, the orders of upper bounds for the deviations of a function and its conjugate from the Cesaro means of their Fourier series are obtained on a class of functions with a given majorant of their k-th modulus of smoothness.

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Literature cited

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    N. K. Bari, Trigonometric Series [in Russian], Moscow (1961).

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    S. B. Stechkin, “Absolute convergence of Fourier series (second report),” Izv. Akad. Nauk SSSR, Ser. Matem.,19, No.4, 221–246 (1955).

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    S. B. Stechkin, “Approximation of periodic functions by Fejer sums,” Tr. Matem. In-ta Akad. Nauk SSSR,62, 48–60 (1961).

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    V. É. Geit, Structural and Constructive Properties of Functions and Their Conjugates [in Russian], Candidate's Dissertation, Sverdlovsk (1970).

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    V. É. Geit, “The accuracy of certain inequalities in the theory of approximation,” Matem. Zametki,10, No. 5, 571–582 (1971).

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    V. É. Geit, “Conditions for imbedding the classes H k,R ω and\(\tilde H_{k,R}^\omega\),” Matem. Zametki,13, No. 2, 169–178 (1973).

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Translated from Matematicheskie Zametki, Vol. 15, No. 1, pp. 15–20, January, 1974.

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Geit, V.É. Order of (C,α)-approximations on certain classes of periodic functions. Mathematical Notes of the Academy of Sciences of the USSR 15, 9–12 (1974). https://doi.org/10.1007/BF01153537

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Keywords

  • Fourier
  • Fourier Series
  • Periodic Function
  • Cesaro Means