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Constructive Approximation

, Volume 4, Issue 1, pp 435–445 | Cite as

Equiconvergence in rational approximation of meromorphic functions

  • Milena P. Stojanova
Article

Abstract

Generalizing the Walsh theorem, E. B. Saff, A. Sharma, and R. S. Varga showed that there is a close relation between the rational interpolants in roots of unity and Padé approximants of certain meromorphic functions. The purpose of this paper is to extend this result, replacing the Padé approximant with other rational functions so as to obtain a larger region of equiconvergence.

AMS classification

41A05 41A20 41A21 

Key words and phrases

Equiconvergence Padé approximation Rational approximation Meromorphic functions 

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References

  1. 1.
    E. B. Saff, A. Sharma, R. S. Varga (1981):An extension to ratioal functions of a theorem of J. L. Walsh on the differences of interpolating polynomials. RATRO Anal. Numér.,15(4):371–390.Google Scholar
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    A. S. Cavaretta Jr., A. Sharma, R. S. Varga (1981):Interpolation in the roots of unity: an extension of a theorem of Walsh. Resultate Math.,3:155–191.Google Scholar
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    R. de Montessus de Ballore (1902):Sur les fractions continues algebriques. Bull. Soc. Math. France,30:28–36.Google Scholar
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    E. B. Saff (1972):An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions. J. Approx. Theory,6:63–67.Google Scholar
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    J. L. Walsh (1969) Interpolation and Approximation by Rational Functions in the Complex Domain, 5th edn. American Mathematical Society Colloquium Publications, vol. 20. Providence, RI: American Mathematical Society.Google Scholar
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    A. Sharma (1986):Some recent results on Walsh theory of equiconvergence. In Approximation Theory V (C. K. Chui, L. L. Schumaker, J. D. Ward, eds.). New York: Academic Press, pp. 173–190.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Milena P. Stojanova
    • 1
  1. 1.Institute of Mathematics and Computer CenterBulgarian Academy of SciencesSofiaBulgaria

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