Complexity in Complex Analysis |
| |
Authors: | Steven R. Bell |
| |
Affiliation: | Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana, 47907-1395, f1bell@math.purdue.eduf1 |
| |
Abstract: | We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces. |
| |
Keywords: | Bergman kernel Szeg? kernel Green's function Poisson kernel. |
本文献已被 ScienceDirect 等数据库收录! |
|