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The Computation of Zeros of Ahlfors Map for Multiply Connected Regions.
- Source :
-
AIP Conference Proceedings . 2017, Vol. 1795 Issue 1, p020003-1-020003-8. 8p. 3 Diagrams, 6 Charts. - Publication Year :
- 2017
-
Abstract
- The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S'(z(t), a) and θ'(t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S'(z(t), a). An integral equation for θ'(t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 1795
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 120673467
- Full Text :
- https://doi.org/10.1063/1.4972147