Mathematical Modelling in Piecewise-Uniform Invironment Based on the Solution of the Markushevich Boundary Problem in the Class of Automorphic Functions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 49-61
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An algorithm for the explicit solution of the Markushevich boundary value problem in the class of automorphic functions with respect of Fuchsian group $\Gamma$ of the second kind is suggested. The boundary condition of the problem is given on the main circle. The coefficients of the tasks are Holder functions. The alqorithm is based on a reduction of the problem to the Hilbert boundary problem. The solution is found in a closed form under additional restriction on the coefficient $b(t)$ of the problem: if $\chi_{+}(t), \chi_{-}(t)$ are factorization multipliers of coefficient $a(t)$, the product of the function $b(t)$ on the quotient of $\overline{\chi_{+}(t)}$ and $\chi_{+}(t)$ is analytic in the domain $D_{-}$ and automorphic with respect to $\Gamma$ in this the domain.
Keywords:
boundary problems for analytic functions, the Markushevich boundary problem, automorphic functions.
@article{VYURU_2013_6_2_a3,
author = {A. A. Patrushev},
title = {Mathematical {Modelling} in {Piecewise-Uniform} {Invironment} {Based} on the {Solution} of the {Markushevich} {Boundary} {Problem} in the {Class} of {Automorphic} {Functions}},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {49--61},
publisher = {mathdoc},
volume = {6},
number = {2},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a3/}
}
TY - JOUR AU - A. A. Patrushev TI - Mathematical Modelling in Piecewise-Uniform Invironment Based on the Solution of the Markushevich Boundary Problem in the Class of Automorphic Functions JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2013 SP - 49 EP - 61 VL - 6 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a3/ LA - ru ID - VYURU_2013_6_2_a3 ER -
%0 Journal Article %A A. A. Patrushev %T Mathematical Modelling in Piecewise-Uniform Invironment Based on the Solution of the Markushevich Boundary Problem in the Class of Automorphic Functions %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2013 %P 49-61 %V 6 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a3/ %G ru %F VYURU_2013_6_2_a3
A. A. Patrushev. Mathematical Modelling in Piecewise-Uniform Invironment Based on the Solution of the Markushevich Boundary Problem in the Class of Automorphic Functions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 49-61. http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a3/