Conformal Mapping of Nonsmooth Domains via the Kerzman–Stein Integral Equation

✍ Scribed by Anthony D. Thomas

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 215 KB
• Volume: 200
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0197

✦ Synopsis

The connection between the Riemann map and the Szego kernel is classical. But the fact that there is an efficient numerical procedure, based on the Kerzman᎐Stein integral equation, for computing the Szego kernel of a smoothly bounded domain in the plane is more recent. In this paper it is shown how to extend the results of Kerzman and Stein to certain nonsmooth domains. This provides a new method for numerically computing the Szego kernel, and hence the Riemann map, of these domains.