The Distribution of Zeros and Poles of Asymptotically Extremal Rational Functions for Zolotarevʹs Problem Original Research Article

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 E1, E2 in the complex plane, the Zolotarev problem entails minimizing the ratio of the sup over E1 of the modulus of a weighted rational to its inf over E2. Potential theoretic tools are utilized in the analysis.