The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis
https://doi.org/10.26907/2541-7746.2024.1.111-122
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
Supporting agencies: This study was supported by the Russian Science Foundation (project no. 23-21-00212)
About the Authors
P. L. Shabalin
Kazan State University of Architecture and Engineering
Russian Federation
Russian Federation
420043; Kazan
R. R. Faizov
Kazan State University of Architecture and Engineering
Russian Federation
Russian Federation
420043; Kazan
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Review
For citations:
Shabalin P.L., Faizov R.R. The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(1):111-122. (In Russ.) https://doi.org/10.26907/2541-7746.2024.1.111-122
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