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The Marchaud inequality for generalized Moduli of smoothness

Polynomial And Rational Approximation

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References

  1. C. de Boor, Splines as linear combination of B-splines, Approximation Theory II, edited by G.G. Lorentz, C.K. Chui and L.L. Schumaker: 1–47, Academic Press, New York 1976.

    Google Scholar 

  2. Z.Ciesielski, Lectures on spline functions (in Polish), Gdańsk University, 1979.

    Google Scholar 

  3. A.O. Gelfond, Calculus of finite differences (in Russian), Fizmatgiz, Moscow 1959.

    Google Scholar 

  4. S. Karlin, W.J. Studden, Tchebysheff systems: with applications in analysis and statistics, Interscience, New York 1966.

    MATH  Google Scholar 

  5. G. Mühlbach, A recurrence formula for generalized divided differences and some applications, J. Approx. Theory 9(1973), 165–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. T. Popoviciu, Sur quelques properties des fonctiones d'une ou deux variables reelles, Mathematica 8(1934), 1–85, Cluj.

    MATH  Google Scholar 

  7. K. Scherer, L.L. Schumaker, A dual basis for L-splines and applications, J. Approx. Theory 29 (1980), 151–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. I.J. Schoenberg, On trigonometric spline interpolation, J. Math. Mech. 13(1964), 795–825.

    MathSciNet  MATH  Google Scholar 

  9. L.L. Schumaker, Spline functions: basic theory, Wiley and Sons, New York 1981.

    MATH  Google Scholar 

  10. P.M.Tamrazov, Smoothness and polynomial approximation (in Russian), Kiev 1975.

    Google Scholar 

  11. A.F.Timan, Theory of approximation of function of a real variable (in Russian) Moscow 1960.

    Google Scholar 

  12. Z. Wronicz, On some properties of LB-splines, Ann. Polon. Math. 46 1985, 381–390.

    MathSciNet  MATH  Google Scholar 

  13. —, Moduli of smoothness associated with Chebyshev systems and approximation by L-splines, Constructive Theory of Functions'84, 906–916, Sofia 1984.

    MATH  Google Scholar 

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© 1987 Springer-Verlag

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Wronicz, Z. (1987). The Marchaud inequality for generalized Moduli of smoothness. In: Gilewicz, J., Pindor, M., Siemaszko, W. (eds) Rational Approximation and its Applications in Mathematics and Physics. Lecture Notes in Mathematics, vol 1237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072460

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  • DOI: https://doi.org/10.1007/BFb0072460

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  • Print ISBN: 978-3-540-17212-3

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