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The Distribution of Zeros and Poles of Asymptotically Extremal Rational Functions for Zolotarev's Problem

✍ Scribed by A.L Levin; E.B Saff

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
161 KB
Volume
110
Category
Article
ISSN
0021-9045

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✦ Synopsis

We investigate the possible limit distributions of zeros and poles associated with ray sequences of rational functions that are asymptotically optimal for weighted Zolotarev problems. For disjoint compacta E 1 , E 2 in the complex plane, the Zolotarev problem entails minimizing the ratio of the sup over E 1 of the modulus of a weighted rational to its inf over E 2 . Potential theoretic tools are utilized in the analysis.

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