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Piecewise polynomial approximation, embedding theorem and rational approximation

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Approximation Theory

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

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References

  1. Th. Bagby and W.P. Ziemer. Pointwise differentiability and absolute continuity. Trans.Amer.Math.Soc. 191 (1974), 129–148.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.S. Birman and M.Z. Solomjak. Piecewise-polynomial approximations of functions of classes W αp . Mat.Sbornik 73, No. 3 (1967), 331–355 = Math.USSR Sb.2 (1967), 295–317.

    MathSciNet  Google Scholar 

  3. Ju.A. Brudnyi. On local best approximations. Dokl.Akad.Nauk SSSR, 161, No. 4 (1965), 746–749 (Russian).

    MathSciNet  Google Scholar 

  4. Ju.A. Brudnyi. A multidimensional analog of a theorem of Whitney. Mat.Sb. 82 (124) (1970), 175–191 = Math.USSR sb. 11(1970), 157–170.

    MathSciNet  MATH  Google Scholar 

  5. Ju.A. Brudnyi. An extension theorem. Func.Anal. and Appl., 4, No. 3 (1970), 97–98 (Russian).

    MathSciNet  Google Scholar 

  6. Ju.A. Brudnyi. Piecewise polynomial approximation and local approximation. Dokl.Akad.Nauk SSSR 201 (1971), 16–18 = Soviet Math.Dokl. 12 (1971), 1591–1594.

    MathSciNet  Google Scholar 

  7. Ju.A. Brudnyi. Spaces defined by means of local approximation. Trudy Moskov.Mat.Obsc. 24 (1971), 69–132 = Trans.Moskow Math. Soc. 24 (1971), 74–139.

    MathSciNet  MATH  Google Scholar 

  8. Ju.A. Brudnyi. On permutation of smooth function. Uspehi Mat.Nauk 27, No. 2 (1972), 165–166 (Russian).

    MathSciNet  Google Scholar 

  9. Ju.A. Brudnyi. Local approximation and differential properties of functions of several variables. Uspehi Mat.Nauk 29, No. 4 (1974), 163–164, (Russian).

    MathSciNet  Google Scholar 

  10. Ju.A. Brudnyi. Spline approximation and functions of bounded variation. Dokl.Akad.Nauk SSSR, 215, No. 3 (1974), 511–513 = Soviet Math.Dokl. 15, No. 2 (1974), 518–521.

    MathSciNet  Google Scholar 

  11. Ju.A.Brudnyi. On scale of L λpq spaces and exact embedding theorems. Proc. Conference of Embedding Theorems (Alma-Ata, 1973), Alma-Ata, 1975 (Russian).

    Google Scholar 

  12. Ju.A. Brudnyi. On extension theorem for some family of functional spaces. Zap.naucn.Semin. LOMI., 56 (1976), 170–173 (Russian).

    MathSciNet  Google Scholar 

  13. Ju.A.Brudnyi. Some nonlinear methods of best approximation. Proc. Intern.Conf.Appr.Theory (Kalouga, 1975). Moskow, 1977 (in preparation).

    Google Scholar 

  14. Ju.A. Brudnyi and I.E. Copengauz. Approximation by piecewise polynomial functions. Uzv.Akad.Nauk SSSR; Ser.Mat. 27 (1963), 723–746 (Russian).

    MathSciNet  Google Scholar 

  15. P.L. Butzer and H. Berens. Semi-Groups of Operators and Approximation. Springer-Verlag, Berlin, 1967.

    Book  MATH  Google Scholar 

  16. G.J. Butler and F.B. Richrds. On Lp saturation theorem for spline. Can.J.Math., 24, No. 5 (1972), 957–966.

    Article  Google Scholar 

  17. A.P. Calderon and A. Zygmund. Local properties of solutions of elliptic partial differential equations. Studia Math., 20 (1961), 171–225.

    MathSciNet  MATH  Google Scholar 

  18. S. Campanato. Proprieta di una famiglia di spazi funzionali. Ann. Scuola Norm. Sup.Pisa, 18 (1964), 137–160.

    MathSciNet  MATH  Google Scholar 

  19. H. Federer. Geometric Measure Theory. Springer-Verlag. New York, 1969.

    MATH  Google Scholar 

  20. G. Freud and V.A. Popov. Some questions of approximation by spline-functions and polynomials. Studia Sci.Math.Hung. 5(1970), 161–171 (Russian).

    MathSciNet  MATH  Google Scholar 

  21. D. Gajer. Saturation bei Spline-Approximation und Quadratur. Numer. Math. 16 (1970), 129–140.

    Article  MathSciNet  MATH  Google Scholar 

  22. A.Jonsson and H.Wallin. A Whithey extension theorem in Lp and Besov space. Dep.Math.Univ.Umea (Publ), 1975, No. 5, 60 pp.

    Google Scholar 

  23. J.-P.Kahane. Theoria constructiva de functiones. Cursos y Semin.Math.Univ.Buenos-Aires, No. 5, 1961.

    Google Scholar 

  24. C.B. Morrey. Functions of several variables and absolute continuity. Duke Math.J., 6 (1940), 187–215.

    Article  MathSciNet  MATH  Google Scholar 

  25. D. Newman. The Zygmund condition for polygonal approximation. Proc.Amer.Math.Soc., 45, No. 2 (1974), 303–303.

    Article  MathSciNet  MATH  Google Scholar 

  26. I. Nitsche. Sätze von Jackson-Bernstein-Tyr für die approximationen mit splines-funktionen. Math.Z., 109, No. 2 (1969), (97–106).

    Article  MathSciNet  Google Scholar 

  27. F.B. Richards. On the saturation class for spline functions. Proc.Amer.Math.Soc., 33, No. 2 (1972), 471–475.

    Article  MathSciNet  MATH  Google Scholar 

  28. K.Scherer. Über die beste approximation von Lp funktionen durch splines. Proc.Intern.Conf. (Varna). Sofia, (1972), 277–286.

    Google Scholar 

  29. O. Shisha. Characterization of functions having Zygmund's property. I.Appr.Theory, 9, No. 9 (1973), 395–397.

    Article  MathSciNet  MATH  Google Scholar 

  30. O. Shisha. Characterization of smoothness properties of functions by means of their degree of approximation by splines. I.Appr.Theory, 12, No. 4 (1974), 365–371.

    Article  MathSciNet  MATH  Google Scholar 

  31. P.L. Ulianov. Imbedding theorems and correlations between best approximations for different metrics. Mat.Sb., 81, No. 1 (1971), 104–131 (Russian).

    Google Scholar 

  32. H. Whitney. On functions with bounded h-th differences. J.Math.Pures and Appl., 9, No. 36 (1957), 67–95.

    MathSciNet  MATH  Google Scholar 

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Authors
  1. Ju. A. Brudnyi
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Robert Schaback Karl Scherer

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© 1976 Springer-Verlag

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Brudnyi, J.A. (1976). Piecewise polynomial approximation, embedding theorem and rational approximation. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087398

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  • DOI: https://doi.org/10.1007/BFb0087398

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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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