Hilbert boundary value problem for generalized analytic functions with a singular line

Abstract

In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient. To solve this problem, we conducted a complete study of the solvability of the Hilbert boundary value problem of the theory of analytic functions with an infinite index due to a finite number of points of a special type of vorticity. Based on these results, we have derived a formula for the general solution and studied the existence and number of solutions to the boundary value problem of the theory of generalized analytic functions.