This article is cited in 13 papers

To the Solution of the Hilbert Problem with Infinite Index

R. B. Salimov, P. L. Shabalin

Kazan State Academy of Architecture and Construction

Abstract: In this paper, we obtain a generalization of the method of regularizing multipliers for the solution of the Hilbert boundary-value problem with finite index in the theory of analytic functions to the case of an infinite power-behaved index. This method is used to obtain a general solution of the homogeneous Hilbert problem for the half-plane, a solution that depends on the existence and the number of entire functions possessing mirror symmetry with respect to the real axis and satisfying some additional constraints related to the singularity characteristic of the index. To solve of the inhomogeneous problem, we essentially use a specially constructed solution of the homogeneous problem whereby we reduce the boundary condition of the Hilbert problem to a Dirichlet problem.

UDC: 517.54

Received: 20.03.2001
Revised: 08.04.2002

DOI: 10.4213/mzm221

 English version: Mathematical Notes, 2003, 73:5, 680–689

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