The Ahlfors map and Szego kernel in multiply connected domains
Abstract
The Ahlfors map of an n-connected domain is a branched, n-to-one map from the domain onto the unit disk. It can be written as the quotient of two kernel functions, the Szegö kernel, and the Garabedian kernel. In the case of an annulus, we locate the zeros of the Ahlfors map and Szegö kernel, as well as the zeros of the derivative of the Ahlfors map. In addition, we are able to write all proper two-to-one maps from the annulus onto the unit disk in terms of a single Ahlfors map. We are also able to locate the double zeros of the Ahlfors map and Szegö kernel in certain special triply connected domains. In more general triply connected domains we have results regarding the location of the zeros. Finally, we compare numerical methods for calculating the Ahlfors map in certain domains.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.