The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis-Reference-Cited by-同舟云学术

The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

Published:2024-04-13 Issue:1 Volume:166 Page:111-122
ISSN:2500-2198
Container-title:Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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Short-container-title:jour

Author:

Shabalin P. L.¹,Faizov R. R.¹

Affiliation:

1. Kazan State University of Architecture and Engineering

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.

Publisher

Kazan Federal University

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