Abstract
This paper deals with differential boundary value problems of elliptic systems, regular solutions of which are called analytic vectors [11]. These problems, in some particular cases, are considered in [1–9]. In [10] the author has studied the differential boundary value problem of linear conjugacy with displacements in simply-connected domain. The purpose of this paper is to extend the study of the problem to the case of multiply-connected domains. First, we solve this problem for Q-holomorphic vectors. In this case a representation formula of solutions to the problem is constructed. In view of this formula we reduce the problem to an equivalent system of singular integral equations and deduce necessary and sufficient conditions for solvability and a formula for the index of the problem for (2-holornorphic vectors. Using Bojarski's formula we reduce the problem in the general case to an analogous problem for Q-holomorphic vectors. The same result about solvability conditions and the index of the problem for generalized analytic vectors can be obtained.
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