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Bernstein theorems for harmonic functions

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Methods of Approximation Theory in Complex Analysis and Mathematical Physics

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References

  1. D. H. Armitage, T. Bagby, and P. M. Gauthier, Note on the decay of elliptic equations, Bull. London Math. Soc. 17 (1985), pp. 554–556.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. H. Armitage and M. Goldstein, Better than uniform approximation on closed sets by harmonic functions with singularities, Proc. London Math. Soc. (4) 60 (1990), pp. 319–343.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Bagby, Approximation in the mean by solutions of elliptic equations, Trans. Amer. Math. Soc. 281 (1984), pp. 761–784.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. S. Baouendi and C. Goulaouic, Approximation of analytic functions on compact sets and Bernstein's inequality, Trans. Amer. Math. Soc. 189 (1974), pp. 251–261.

    MathSciNet  MATH  Google Scholar 

  5. T. Bloom, On the convergence of multivariate Lagrange interpolants, Constructive Approximation 5 (1989), pp. 415–435.

    Article  MathSciNet  MATH  Google Scholar 

  6. J.-P. Demailly, Measures de Monge-Ampère et mesures plurisousharmoniques, Math. Zeitschrift 194 (1987), pp. 519–564.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Dineen, The Schwarz lemma, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1989.

    MATH  Google Scholar 

  8. R. Harvey and J. C. Polking, A Laurent expansion for solutions to elliptic equations, Trans. Amer. Math. Soc. 180 (1973), pp. 407–413.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. France 113 (1985), pp. 231–240.

    MathSciNet  MATH  Google Scholar 

  10. M. Klimek, Pluripotential theory, to appear.

    Google Scholar 

  11. Nguyen Thanh Van and B. Djebbar, Propriétés asymptotiques d'une suite orthonormale de polynomes harmoniques, Bull. Sc. math. (5) 113 (1989), pp. 239–251.

    MATH  Google Scholar 

  12. W. Plesniak, On some polynomial conditions of the type of Leja in Cn, in Analytic functions Kozubnik 1979, Proceedings, Lecture Notes in Mathematics vol. 798, Springer-Verlag, pp. 384–391.

    Google Scholar 

  13. J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), pp. 322–357.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Siciak, Asymptotic behavior of harmonic polynomials bounded on a compact set, Ann. Polon. Math. 20 (1968), pp. 267–278.

    MathSciNet  MATH  Google Scholar 

  15. J. Siciak, Extremal plurisubharmonic functions in CN, Ann. Polon. Math. 39 (1981), pp. 175–211.

    MathSciNet  MATH  Google Scholar 

  16. J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Coll. Publ. vol. 20, Third Edition, 1960.

    Google Scholar 

  17. J. L. Walsh, The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Bull. Amer. Math. Soc. 35 (1929), pp. 499–544.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. L. Walsh, Maximal convergence of sequences of harmonic polynomials, Ann. of Math. 38 (1937), pp. 321–364.

    Article  MathSciNet  MATH  Google Scholar 

  19. V.P. Zaharjuta, Extremal plurisubharmonic functions, orthogonal polynomials and Bernstein-Walsh theorem for analytic functions of several complex variables, Ann. Polon. Math. 33 (1976), pp. 137–148.

    MathSciNet  Google Scholar 

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Andrei A. Gonchar Edward B. Saff

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© 1993 The Euler International Mathematical Institute

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Bagby, T., Levenberg, N. (1993). Bernstein theorems for harmonic functions. In: Gonchar, A.A., Saff, E.B. (eds) Methods of Approximation Theory in Complex Analysis and Mathematical Physics. Lecture Notes in Mathematics, vol 1550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0117470

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  • DOI: https://doi.org/10.1007/BFb0117470

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56931-2

  • Online ISBN: 978-3-540-47792-1

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