The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis
| Autor: | P. L. Shabalin, R. R. Faizov |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Учёные записки Казанского университета. Серия Физико-математические науки, Vol 166, Iss 1, Pp 111-122 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2541-7746 2500-2198 |
| DOI: | 10.26907/2541-7746.2024.1.111-122 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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