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The computation of zeros of Ahlfors map for multiply connected regions

Nazar, Kashif and Mohamed Murid, Ali Hassan and Kareem Sangawi, Ali Wahab (2016) The computation of zeros of Ahlfors map for multiply connected regions. In: International Conference & Workshop on Mathematical Analysis (ICWOMA 2016), 2016.

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Official URL: http://dx.doi.org/10.1063/1.4972147

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

Item Type:Conference or Workshop Item (Paper)
Additional Information:RADIS System Ref No:PB/2016/10611
Uncontrolled Keywords:exact zeros, values
Subjects:Q Science
Divisions:Science
ID Code:66738
Deposited By: Fazli Masari
Deposited On:22 Nov 2017 08:45
Last Modified:22 Nov 2017 08:45

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