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Салимов Р. Б. To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., , vol. , iss. , pp. 9-?.

Heading: 
Mathematics

To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case

Authors: 
Salimov Rasikh Bakhtigareevich, Kazan State University of Architecture and Engineering, Kazan State University of Architecture and Engineering, Russia, 420043, Kazan, Zelenaya st., 1 , salimov.rsb@gmail.com
Abstract: 

The author offers a new approach to solution of the Riemann–Hilbert boundary value problem for analytic function in multiconnected

circular domain. This approach is based on construction of solution of corresponding homogeneous problem, when analytic in domain

function is being defined by known boundary values of its argument. The author considers a special case of a problem when the

index of a problem is more than zero and on unit of less order of connectivity of domain. Resolvability of a problem depends on

number of solutions of some system of the linear algebraic equations.

Key words: 
Riemann–Hilbert boundary value problem, index of a problem, Schwarz’s operator.
References

1. Salimov R. B. Modification of new approach to solution of the Hilbert boundary value problem for analytic function in multi-connected circular domain. Izv. Saratov. Univ. N.S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 1, pp. 32–38 (in Russian). 2. Vekua I. N. Generalized analytic functions. Oxford, Pergamon Press, 1962, 668 p. (Rus. ed.: Vekua I. N. Obobshchennye analiticheskie funktsii. Moscow, Fizmatgiz, 1959, 628 p.) 3. Gahov F. D. Boundary-Value Problems. Moscow, Nauka, 1977, 640 p. (in Russian). 4. Muskhelishvili N. I. Singular Integral Equations. Boundary-Value Problems of the Theory of Functions and Some of Their Applications to Mathematical Physics. Moscow, Nauka, 1968, 511 p. (in Russian). 5. Salimov R. B. Some properties of analytic in a disc functions and their applications to study of behaviour of singular integrals. Russian Math. (Izvestiya VUZ. Matematika), 2012, vol. 56, no. 3, pp. 36–44.

Short text (in English): 
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