Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2003; 40(3): 447-460

Printed May 1, 2003

Copyright © The Korean Mathematical Society.

Algebraic kernel functions and representation of planar domains

Moonja Jeong and Masahiko Taniguchi

The University of Suwon and Kyoto University

Abstract

In this paper we study the non-degenerate $n$-connected canonical domains with $n>1$ related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szeg\H o kernel. We characterize the non-degenerate doubly connected canonical domains.

Keywords: conformal representation, Ahlfors map, Bergman kernel, Szeg\H o kernel, algebraic function, canonical domain

MSC numbers: Primary 32G10, 32G15, 30C40; Secondary 30C20, 30F60