The approximate conformal mapping onto multiply connected domains
Journal Title: Проблемы анализа-Issues of Analysis - Year 2019, Vol 8, Issue 1
Abstract
The method of boundary curve reparametrization is generalized to the case of multiply connected domains. We construct the approximate analytical conformal mapping of the unit disk with N circular slits or an annulus with (N - 1) circular slits onto an arbitrary (N + 1) multiply connected finite domain with a smooth boundary. The method is based on the solution of the Fredholm equation. This solution is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a set of Laurent polynomials in the set of annular regions The method is easily computable.
Authors and Affiliations
D. Abzalilov, E. Shirokova
Keywords
Related Articles
- EP ID EP493210
- DOI 10.15393/j3.art.2019.5050
- Views 81
- Downloads 0
РАЗЛОЖЕНИЕ ПО СОБСТВЕННЫМ ФУНКЦИЯМ ДЛЯ НЕКОТОРЫХ ФУНКЦИОНАЛЬНО-ДИФФЕРЕНЦИАЛЬНЫХ ОПЕРАТОРОВ
We prove the completness of the eigenfunctions of some boundary function-differental problems.
WILKER AND HUYGENS-TYPE INEQUALITIES INVOLVING GUDERMANNIAN AND THE INVERSE GUDERMANNIAN FUNCTIONS
Five Wilker Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions are obtained. The Schwab-Borchardt mean plays a crucial role in the proofs. Also, an analytical inequality for the sums...
INEQUALITIES CONNECTING GENERALIZED TRIGONOMETRIC FUNCTIONS WITH THEIR INVERSES
Motivated by the recent work [1], in this paper we study the relations of generalized trigonometric and hyperbolic functions of two parameters with their inverse functions.
ON THE INEQUALITIES FOR THE VOLUME OF THE UNIT BALL Ω_N IN R^N
The inequalities about the volume of the unit ball Ω_n in R^n were studies by several authors, especially Horst Alzer has a great contribution to this topic. Thereafter many authors produced numerous papers on this topic...
About a structure of exponential monomials on some locally compact abelian groups
We describe the structure of some class of exponential monomials on some locally compact abelian groups. The main result of the paper is the next theorem.