The Riemann boundary value problem in a half-plane for generalized analytic functions with a supersingular line
Abstract
We study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for one generalized Cauchy-Riemann equation with a strong coefficient singularity. To solve this problem, it was necessary to derive a structural formula for the general solution of the equation and conduct a complete study of the solvability of the Riemann boundary value problem for analytical functions with an infinite power-order index. Based on this study, a general solution formula and a picture of the solvability of the boundary value problem for generalized analytical functions are derived.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Analytic and geometric function theory
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Russian Mathematics
- Issue
- 2
- Pages
- 63–73
- Publication date
- 10 March 2026
- Language
- EN