Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Salimov R. B., Shabalin P. L. The M.A. Lavrentiev Inverse Problem on Mapping of Half-Plane Onto Polygon with Infinite Set of Vertices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 1, pp. 23-31. DOI: 10.18500/1816-9791-2010-10-1-23-31

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
18.01.2010
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Language: 
Russian
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UDC: 
517.54

The M.A. Lavrentiev Inverse Problem on Mapping of Half-Plane Onto Polygon with Infinite Set of Vertices

Autors: 
Salimov Rasikh Bakhtigareevich, Kazan State University of Architecture and Engineering
Shabalin Pavel Leonidovich, Kazan State University of Architecture and Engineering
Abstract: 

The authors consider a generalization of the M.A.Lavrentiev inverse problem on a conformal mapping of half-plane onto interiority of a polygon for the case where the set of vertices of this polygon is infinite. We assume that the inner angles at unknown vertices and the image of the vertices under the conformal mapping on the real line are given. Under certain restrictions on values of the angles and on the sequence of points of the real line that are preimages of the vertices the formula for such a mapping is obtained.  

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