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Equiconvergence in rational approximation of meromorphic functions. (English) Zbl 0677.41003
The result of E. B. Saff, A. Sharma and R. S. Varga [RAIRO, Anal. Numér. 15, 371-390 (1981; Zbl 0485.41003)] is extended in the same manner as the theorem of A. S. Cavaretta, A. Sharma and R. S. Varga [Result. Math. 3, 155-191 (1981; Zbl 0447.30020)] generalizes Walsh’s theorem on equiconvergence. The rate of equiconvergence of rational interpolants in the roots of unity and of the introduced rational interpolants coincides with one from Cavaretta’s, Sharma’s and Varga’s theorem. The correctness of the definition of the introduced rational interpolants for a class of meromorphic functions is proved.
Reviewer: A.Lukashov

41A05 Interpolation in approximation theory
41A21 Padé approximation
41A20 Approximation by rational functions
Full Text: DOI
[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. · Zbl 0485.41003
[2] 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. · Zbl 0447.30020
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[5] 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.
[6] 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. · Zbl 0612.42011
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