ASYMPTOTIC-BEHAVIOR OF ZEROS OF BIEBERBACH POLYNOMIALS

[摘要] Let OMEGA be a simply-connected domain in the complex plane and let pi-n denote the nth-degree Bieberbach polynomial approximation to the conformal map f of OMEGA onto a disc. In this paper we investigate the asymptotic behaviour (as n --> infinity) of the zeros of pi-n, pi-n' and also of the zeros of certain closely related rational approximants to f. Our results show that, in each case, the distribution of the zeros is governed by the location of the singularities of the mapping function f in C/OMEGA, and we present numerical examples illustrating this.

[发布日期] 1991-04-26

[关键词] BIEBERBACH POLYNOMIALS;BERGMAN KERNEL FUNCTION;CONFORMAL MAPPING;ZEROS OF POLYNOMIALS