A new approach to solving homogeneous Riemann boundary-value problem on a ray with infinite index

We consider a Riemann boundary-value problem with infinite Gakhov’s index. The boundary data are defined on positive ray of the real axis. We solve the problem by means of removal of singularity of boundary data at the infinity. This approach is analogous to Gakhov’s method of elimination of singularities in the problemswith finite indices, but we use another eliminating factors.