Classes of univalent and multivalent Schwarz-Christoffel integrals and their applications
type: Item
instance of: scholarly article
title: Classes of univalent and multivalent Schwarz-Christoffel integrals and their applications
zbMATH Open document ID: 0906.30014
author: L. A. Aksent'ev
author: G. G. Bil'chenko
author: F. G. Avkhadiev
published in: Russian Mathematics
publication date: 1998-10-18T00:00:00Z
review text: The authors present the scheme of proof of the following theorem: Given a set of reals \(\{\alpha_k\}^n_{k=1}\) satisfying the conditions \(0<\alpha_k<2\), \(\sum^n_{k=1} \alpha_k =n-2\), there exists an ordered set of distinct complex numbers \(\{a_k\}^n_{k=1}\), \(a_k =e^{i\varphi_k}\), \(0\leq \varphi_1< \varphi_2< \cdots <\varphi_n <2\pi\), such that the function \( f(z)= C_1\int^z_0 \prod^n_{k=1} (z-a_k)^{\alpha_k-1} dz+C_2\), \(C_1\neq 0\); \(C_1, C_2\in \mathbb{C}\) univalently maps the closed disk \(\overline E= \{z:| z|\leq 1\} =E\cup \partial E\) onto the polygon \(\overline D_n(\alpha_1, \alpha_2, \dots, \alpha_n)\). The result is applied to univalent solvability of the inverse boundary value problems with polygonal boundary, to the univalent variation of the Cisotti formula and classes of multivalent solutions of the Hilbert boundary value problem.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30E25
zbMATH DE Number: 1175166
zbMATH Keywords: inverse boundary value problems
zbMATH Keywords: Hilbert boundary value problem
reviewed by: Zbigniew Binderman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1175166