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On the Convergence of Rational Functions of Best Lp-Approximation

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Abstract

In the present paper, for sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of best Lp — approximation of a function ƒ(z) ∈ Lp(Γ), with Γ being a closed rectifiable analytic curve, are considered. The case ƒ(z) ∈ Hp is discussed, too.

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References

  1. G. M. Golusin, Geometric Theory of Functions of a Complex Variable, in Russian, Nauka, Moscow, 1966.

    Google Scholar 

  2. A. A. Gonchar, A Local Conjecture for the Uniqueness of Analytic Functions, in Russian, Matem. Sbornik, 89(1972), 148–164.

    Google Scholar 

  3. H. Gonska, R. K. Kovacheva, An Extension of Montel’s Theorems to Some Rational Approximating Sequences, Bulletin de la Societe des Sciences et des Lettres de Lodz, 1996, Vol. XXI, 73–86.

    MathSciNet  MATH  Google Scholar 

  4. R. G rothmann and E. B. Saff, On the Behavior of Zeros and Poles of Best Uniform Polynomial and Rational Approximation, Nonlinear Numerical Methods and Rational Approximations, D.Reidel Publ. Co., Dordrecht, Holland (1988), 57–77.

    Book  Google Scholar 

  5. R. K. Kovacheva, Diagonal Rational Chebyshev Approximants and Holomorphic Continuation of Functions, Analysis 10, 1990, 147–161.

    Article  MathSciNet  MATH  Google Scholar 

  6. I. P. Natanson, The Theory of Analytic Functions, in Russian, Nauka, Moscow, 1950.

    Google Scholar 

  7. I. I. Privalov, Boundary Properties of Analytic Functions, in Russian, Nauka, Moscow, 1950.

    Google Scholar 

  8. J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Plane, AMS Colloquium Publications, Volume XX, 1960; Translation in Russian, IL, Moscow, 1969.

  9. J. L. Walsh, Overconvergence, Degree of Convergence and Zeros of Sequences of Analytic Functions, Duke Math. J. 13(1946), 195–235.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Zygmund, Trigonometric Series, Cambridge, At the University Press, 1959

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ralitza K. Kovacheva

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  1. Ralitza K. Kovacheva
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Kovacheva, R.K. On the Convergence of Rational Functions of Best Lp-Approximation. Results. Math. 36, 271–280 (1999). https://doi.org/10.1007/BF03322116

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  • DOI: https://doi.org/10.1007/BF03322116

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