The solution of the homogeneous Riemann boundary value problem with a countable set of points of discontinuity of the first kind its coefficient

We consider the Riemann homogeneous boundary value problem with a countable set of points of discontinuity of the first kind in the case, when it is required to find two functions, analytic, respectively, in the upper and lower half-plane, for a given linear boundary condition on the real axis, connecting the boundary values of the unknown functions.