A numerical method for locating the zeros of ahlfors map for doubly connected regions
The Ahlfors map and Szeg¨o kernel are both classically related to each other. Ahlfors map can be computed using Szeg¨o kernel without relying on the zeros of Ahlfors map. The Szeg¨o kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/61627/ http://www.icsccm.com/2015/WB/ |
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| Summary: | The Ahlfors map and Szeg¨o kernel are both classically related to each other. Ahlfors map can be computed using Szeg¨o kernel without relying on the zeros of Ahlfors map. The Szeg¨o 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 unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szeg¨o kernel, its derivative and the derivative of boundary correspondence function of Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method. |
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