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Upper bounds for the best one-sided approximation by splines of the classes WrL1

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Abstract

In the present note we will investigate the problem of the one-sided approximation of functions by n-dimensional subspaces. In particular, we will find the exact value of the best one-sided approximation of the class WrL1 (r=1, 2, ...) of all periodic functions f(x) of period 2π for which f(r−1)(x) (f(0)(x)=f(x)) is absolutely continuous and ∥f(r)∥L1≤1 by periodic spline functions S2nμ (μ = 0, 1, ..., n=1, 2, ...) of period 2π, order μ,and deficiency 1.

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Literature cited

  1. T. Ganilius, “On one-sided approximation by trigonometric polynomials,” Math. Scand.,4, 247–258 (1966).

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  2. N. I. Akhiezer, Lectures on Theory of Approximation [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  3. V. A. Kaminskii, “The problem of conditional minimum of a sublinear functional in a Banach space with a cone,” Proceedings of the Central Zonal Union of Mathematical Professorials, Kalinin (1970), pp. 99–107.

  4. E. G. Gol'shtein, Duality Theory in Mathematical Programming and Its Applications [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  5. A. A. Ligun, “Exact inequalities for the supremums of seminorms on classes of periodic functions,” Matem. Zametki,13, No. 5, 647–654 (1973).

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  6. S. M. Nikol'skii, “Approximation of functions by trigonometric polynomials in the mean,” Izv. Akad. Nauk SSSR, Ser. Matem.,10 (1946).

  7. V. G. Doronin, “One-sided approximation of a class of periodic functions,” in: Scientific Works of Dnepropetrovsk State University, Matematika i Mekhanika, 26–28 (1972).

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Authors and Affiliations

  1. Dnepropetrovsk State University, USSR

    V. G. Doronin & A. A. Ligun

  2. Dneprodzershinsk Industrial Institute, USSR

    V. G. Doronin & A. A. Ligun

Authors
  1. V. G. Doronin
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  2. A. A. Ligun
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Translated from Matematicheskie Zametki, Vol. 19, No. 1, pp. 11–17, January, 1976.

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Doronin, V.G., Ligun, A.A. Upper bounds for the best one-sided approximation by splines of the classes WrL1 . Mathematical Notes of the Academy of Sciences of the USSR 19, 7–10 (1976). https://doi.org/10.1007/BF01147610

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  • DOI: https://doi.org/10.1007/BF01147610

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