Inhomogeneous Hilbert Boundary-Value Problem with a Finite Number of Second-Type Singularity Points

In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points at which the argument of the coefficient function has second-type discontinuities (of a power order with exponent $<1$). We obtain formulas for the general solution of the inhomogeneous problem and discuss the existence and uniqueness of the solution. The study is based on the theory of entire functions and the geometric theory of functions of a complex variable.