Homogeneous Hilbert boundary-value problem with several points of turbulence

Abstract

We consider Riemann–Hilbert boundary value problem with infinite index in unit disk. Its coefficient is Hölder-continuous everywhere on the unit circle excluding a finite set of points, where its argument has power discontinuities of order less one. The present article is the first research of this version of Hilbert boundary-value problem with infinite index. We obtain formulas for its general solution, investigate existence ad uniqueness of solutions, and describe the set of solutions in the case of non-uniqueness. Our technique is based on theory of entire functions and geometric theory of functions.