The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

Abstract

This article analyzes the inhomogeneous Hilbert boundary value problem for an upper half-plane with the finite index and boundary condition on the real axis for one generalized Cauchy–Riemann equation with a singular point on the real axis. A structural formula was obtained for the general solution of this equation under restrictions leading to an infinite index of the logarithmic order of the accompanying Hilbert boundary value problem for analytic functions. This formula and the solvability results of the Hilbert problem in the theory of analytic functions were applied to solve the set boundary value problem.

Keywords

• hilbert boundary value problem
• generalized analytic functions
• singular point
• infinite index
• entire functions of refined zero order