Gafai, Nuraddeen S. and Mohamed Murid, Ali Hassan and Naqos, Samir and A. Wahid, Nur H. A.
(2023)
*Computing the zeros of the Szegö kernel for doubly connected regions using conformal mapping.*
AIMS Mathematics, 8
(5).
pp. 12040-12061.
ISSN 2473-6988

PDF
480kB |

Official URL: http://dx.doi.org/10.3934/math.2023607

## Abstract

An explicit formula for the zero of the Szegö kernel for an annulus region is well-known. There exists a transformation formula for the Szegö kernel from a doubly connected region onto an annulus. Based on conformal mapping, we derive an analytical formula for the zeros of the Szegö kernel for a general doubly connected region with smooth boundaries. Special cases are the explicit formulas for the zeros of the Szegö kernel for doubly connected regions bounded by circles, limacons, ellipses, and ovals of Cassini. For a general doubly connected region with smooth boundaries, the zero of the Szegö kernel must be computed numerically. This paper describes the application of conformal mapping via integral equation with the generalized Neumann kernel for computing the zeros of the Szegö kernel for smooth doubly connected regions. Some numerical examples and comparisons are also presented. It is shown that the conformal mapping approach also yields good accuracy for a narrow region or region with boundaries that are close to each other.

Item Type: | Article |
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Uncontrolled Keywords: | conformal mapping, doubly connected regions, generalized Neumann kernel, integral equation, Szegö kernel |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 104964 |

Deposited By: | Widya Wahid |

Deposited On: | 01 Apr 2024 06:31 |

Last Modified: | 01 Apr 2024 06:31 |

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