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Best approximation by splines on classes of periodic functions in the metric of L

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Abstract

We have obtained the exact value of the upper bound on the best approximations in the metric of L on the classes WrHω of functionsf ∈C r2π for which ¦f (r) (x′)-f (r) (x″)”) ¦ <ω(¦ x′-x″f) [ω (t) is the upwards-convex modulus of continuity] by subspaces of r-th order polynomial splines of defect 1 with respect to the partitioning kπ/n.

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Literature cited

  1. N. P. Korneichuk, “On the uniform approximation of periodic functions by subspaces of finite dimension,” Dokl. Akad. Nauk SSSR,213, No. 3, 525–528 (1973).

    Google Scholar 

  2. N. P. Korneichuk, “On the diameters of classes of continuous functions in space Lp,” Mat. Zametki,10, No. 5, 493–500 (1971).

    Google Scholar 

  3. S. M. Nikol'skii, “Approximation of functions by trigonometric polynomials with a mean,” Izv. Akad. Nauk SSSR, Ser. Matem.,10, 207–256 (1946).

    Google Scholar 

  4. A. N. Kolmogorov, “On inequalities between the upper bounds of sequences of arbitrary functions on the infinite interval,” Uch. Zap. Moskowsk. Gos. Univ., Ser. Matem.,30, No. 3, 3–13 (1939).

    Google Scholar 

  5. E. M. Stein, “Functions of exponential type,” Ann. Math.,65, No. 3, 582–592 (1957).

    Google Scholar 

  6. N. P. Korneichuk, “Extremal values of functionals and best approximation on classes of periodic functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 1, 93–124 (1971).

    Google Scholar 

  7. N. P. Korneichuk, “Inequalities for differentiable periodic functions and the best approximation of one class of functions by another,” Izv. Akad. Nauk SSSR, Ser. Matem.,36, No. 2, 423–434 (1972).

    Google Scholar 

  8. N. P. Korneichuk, “On methods for investigating the extremal problems of the theory of best approximation,” Usp. Mat. Nauk,29, No. 3, 9–42 (1974).

    Google Scholar 

  9. V. P. Motornyi and V. I. Ruban, “The diameters of certain classes of differentiable periodic functions in space L.,” Mat. Zametki,17, No. 4, 531–543 (1975).

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, USSR

    N. P. Korneichuk

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  1. N. P. Korneichuk
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Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 655–664, November, 1976.

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Korneichuk, N.P. Best approximation by splines on classes of periodic functions in the metric of L. Mathematical Notes of the Academy of Sciences of the USSR 20, 927–933 (1976). https://doi.org/10.1007/BF01146912

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  • DOI: https://doi.org/10.1007/BF01146912

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