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On the approximation by Chebyshev splines in the metric of L p , p > 0

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Abstract

We prove a direct Jackson estimate for the approximation by Chebyshev splines in the classes L p , p > 0.

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References

  1. S. Karlin, Total Positivity and Applications, Stanford University Press, Stanford (1968).

    Google Scholar 

  2. H. Johnen and K. Sherer, “Direct and inverse theorems for best approximations by A-splines,” in: K. Böhmer, G. Meinardus, and W. Schemp (editors), Spline Functions, Lect. Notes Math., 501 (1975), pp. 116–131.

  3. L. L. Schumaker, Spline Functions: Basic Theory, Wiley, New York (1968).

    Google Scholar 

  4. Z. Wronich, “Moduli of smoothness associated with Chebyshev systems and approximation by L-splines,” in: Bl. Sendov, P. Petrushev, R. Maleev, and S. Tashev (editors), Constructive Theory of Functions’84, Sofia (1984), pp. 906–916.

  5. Z. Wronich, Chebyshevian Splines, Jisse Math. CCCV, Warszawa (1990).

    Google Scholar 

  6. E. A. Storozhenko and P. Oswald, “Jackson theorem in the spaces Lp(Rk), 0 < p < 1,” Sib. Mat. Th., 4, 888–901 (1978).

    Google Scholar 

  7. P. Oswald, “Approximation by splines in the metric of Lp, 0 < p < 1,” Math. Nachr., 94, 69–96 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  8. E. A. Storozhenko and Yu. V. Kryakin, On the Whitney theorem in Lp-metric,” Mat. Sb., 186, No. 3, 131–142 (1995).

    MathSciNet  Google Scholar 

  9. Yu. V. Kryakin, Approximation of Functions on a Unit Circle in the Spaces L p and H p [in Russian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Odessa (1985).

    Google Scholar 

  10. T. Popoviciu, “Sur la reste dans certaines formulas lineaires d’approximation de l’analyse,” Math. Cluj., 1 (24), 95–142 (1959).

    MathSciNet  Google Scholar 

  11. H. Whitney, “On functions with bounded nth differences,” J. Math. Pure Appl., 36, 67–95 (1955).

    MathSciNet  Google Scholar 

  12. V. Kh. Sendov and V. A. Popov, “On classes characterized by the best approximation by spline functions,” Mat. Zametki, 8, No. 2, 137–148 (1970).

    MATH  MathSciNet  Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.50, No. 9, pp. 1193–1201, September, 1998.

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Kryakin, Y.V. On the approximation by Chebyshev splines in the metric of L p , p > 0. Ukr Math J 50, 1365–1375 (1998). https://doi.org/10.1007/BF02525243

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  • DOI: https://doi.org/10.1007/BF02525243

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