Cite this article as:
Salimov R. B. 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., 2013, vol. 13, iss. 3, pp. 52-58. DOI: https://doi.org/10.18500/1816-9791-2013-13-3-52-58
To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case
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.
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.
