Regions of meromorphy determined by the degree of best rational approximation
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- by E. B. Saff PDF
- Proc. Amer. Math. Soc. 29 (1971), 30-38 Request permission
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.References
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A. I. Markuševič, Theory of functions of a complex variable. Vol. 3, GITTL, Moscow, 1950; English transl., Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 12, 87; MR 35 #6799.
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 30-38
- MSC: Primary 30.70
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281930-2
- MathSciNet review: 0281930