Boundary-value problem of Сarleman with a noninvolutory shift

By a conformal pasting method we reduce the Carleman boundary-value problem
$$ \Phi^+[\alpha(t)]=G(t)\Phi^+(t)+g(t) $$
with a nonconvergent shift $\alpha(t)$ ($\alpha[\alpha(t)]\not\equiv t$) to the problem of finding all analytic functions which are simultaneously the solutions of two problems on an open contour: the Riemann problem and the Hasemann problem. Using this reduction, we obtain a theorem concerning the solvability of the stated problem.