Brief communications

The Hilbert boundary value problem for generalized analytic functions with a supersingular line

P. L. Shabalin^a, A. M. Gazizov<sup>b

a</sup> Kazan State University of Architecture and Engineering, 1 Zelenaya str., Kazan, 420032 Russia
^b Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: This paper studies the nonhomogeneous Hilbert boundary value problem in the half-plane with a finite index for a single generalized Cauchy–Riemann equation with a strong singularity in the coefficient. A formula for the solution of this equation is derived, and the solvability of the Hilbert problem for analytic functions with an infinite index and two vortex points of power and logarithmic orders is investigated. Based on this, the solvability of the Hilbert boundary value problem for generalized analytic functions is studied.

Keywords: Hilbert boundary value problem, generalized analytic function, infinite index, entire function.

UDC: 517.54

Received: 16.06.2025
Revised: 16.06.2025
Accepted: 18.06.2025

DOI: 10.26907/0021-3446-2025-8-92-98