The distribution of zeros and poles of asymptotically extremal rational functions for Zolotarev's problem

Authors
Levin, AL Saff, EB
Citation
Al. Levin et Eb. Saff, The distribution of zeros and poles of asymptotically extremal rational functions for Zolotarev's problem, J APPROX TH, 110(1), 2001, pp. 88-108
Citations number
6
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
110
Issue
1
Year of publication
2001
Pages
88 - 108
Database
ISI
SICI code
0021-9045(200105)110:1<88:TDOZAP>2.0.ZU;2-4
Abstract
We investigate the possible limit distributions of zeros and poles associat ed with ray sequences of rational functions that are asymptotically optimal for weighted Zolotarev problems. For disjoint compacta E-1, E-2 in the com plex plane, the Zolotarev problem entails minimizing the ratio of the sup o ver E-1 of the modulus of a weighted rational to its inf over E-2. Potentia l theoretic tools are utilized in the analysis. (C) 2001 Academic Press.