Brief communications

A direct method of solving the singular integral equation with the Hilbert kernel

V. P. Kadushin^a, A. I. Shakirov<sup>b

a</sup> Chair of Theory of Functions and Approximations, Kazan State University, Kazan, Russia
^b TGT Oil & Gas Services, Ltd.

Abstract: In this paper we consider a class of singular integral second-kind equations with Hilbert kernel on the unit circumference. We theoretically justify a method based on an interpolation-type operator.

Keywords: Lebesgue space, integral equation, singular integral with the Hilbert kernel, convergence, error estimate.

UDC: 517.51+517.96+519.64

Received: 14.09.2007
Revised: 31.03.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:6, 53–57

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