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Approximative properties of splines

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Approximation Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 556))

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References

  1. H.B. Curry, I.J. Schoenberg, On Pólya functions IV: The fundamental spline functions and their limits, J.d'Analyse Math. 17(1966), 71–107.

    Article  MathSciNet  MATH  Google Scholar 

  2. I.J. Schoenberg, Cardinal interpolation and spline functions, J.Approximation Theory, 2(1969). 167–206.

    Article  MathSciNet  MATH  Google Scholar 

  3. J.R. Rice, the approximation of functions, Vol. II, Addison-Wesley, Reading, 1969.

    MATH  Google Scholar 

  4. J. Domsta, A theorem on B-splines, Studia Math., T. XLI (1972), 291–314.

    MathSciNet  MATH  Google Scholar 

  5. Ju.N. Subbotin, Extremal functional interpolation and spline approximation, Math. zametki, 16, N 5 (1974), 843–854.

    MathSciNet  MATH  Google Scholar 

  6. Ju.N.Subbotin, Extremal functional interpolation and spline approximation, Thesis, Sverdlovsk, 1973.

    Google Scholar 

  7. K. Scherer, On Bernstein's inequalities in Banach space, Math.zametki, 17, N 6 (1975), 925–937.

    MathSciNet  Google Scholar 

  8. J.H. Ahlberg, E.N. Nilson, J.L. Walsh, The theory of splines and their applications, Academic Press, New York and London, 1967.

    MATH  Google Scholar 

  9. Z. Ciesielski, Properties of the orthonormal Franklin system, II, Studia Math. 27 (1966), 289–323.

    MathSciNet  MATH  Google Scholar 

  10. Z. Ciesielski, J. Domsta, Construction of an orthonormal basis in Cm(Id) and W mp (Id), Studia Math., T. XLI (1972) 211–224.

    MathSciNet  MATH  Google Scholar 

  11. S.Banach, Théorie des opérations linéaires, Warszawa, 1932.

    Google Scholar 

  12. P. Enflo, A conterexample to the approximation problem in Banach spaces, Acta math., Vol. 130, N 3–4 (1973), 309–317.

    Article  MathSciNet  MATH  Google Scholar 

  13. S.V. Bockarjov, Existence of basis in space of analytic in a circle functions and some properties of Franklin's system (Russian), Math. Sbornik, V.95 (137), 1 (1974), 3–18.

    Google Scholar 

  14. I.P.Natanson, Constructive theory of function. M-L., 1949.

    Google Scholar 

  15. S.B. Steckin, On the order of best approximation of continuous functions, Isvestia AN USSR (Ser.Math.) 15 (1951), 219–242.

    MathSciNet  Google Scholar 

  16. S.M. Nikolskij, Generalization of one Bernstein's inequality, Dokl. AN USSR, 60, N 9 (1948), 1507–1510.

    Google Scholar 

  17. S.B. Steckin, Generalization of some Bernstein's inequalities, Dokl. AN USSR, 60 (1948), 1511–1514.

    MathSciNet  Google Scholar 

  18. Ju.N. Subbotin, On the relations between finite differences and the corresponding derivatives, Proc. Steklov Inst. Math., 78 (1965), pp. 24–42.

    MathSciNet  Google Scholar 

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Authors
  1. Ju. N. Subbotin
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Robert Schaback Karl Scherer

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© 1976 Springer-Verlag

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Subbotin, J.N. (1976). Approximative properties of splines. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087423

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  • DOI: https://doi.org/10.1007/BFb0087423

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08001-5

  • Online ISBN: 978-3-540-37552-4

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