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Proceedings of the American Mathematical Society

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Regions of meromorphy determined by the degree of best rational approximation

Author: E. B. Saff
Journal: Proc. Amer. Math. Soc. 29 (1971), 30-38
MSC: Primary 30.70
MathSciNet review: 0281930
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Abstract: In this paper we investigate the relationship between the degree of best rational approximation to a given function $ f(z)$ and the regions in which $ f(z)$ is meromorphic. We show, for example, that if rational functions $ {r_{nv}}(z)$ of respective types (n, v), i.e., rational functions with v free poles, converge geometrically (as $ n \to \infty $) to $ f(z)$ on a closed Jordan region E, then $ f(z)$ must be meromorphic in a region which contains E in its interior.

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Keywords: Regions of meromorphy, best rational approximation, closed Jordan region, rational function of type (n, v), polynomial of least squares approximation, Faber polynomials
Article copyright: © Copyright 1971 American Mathematical Society