Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions

Abstract

In this paper we study some classes of generalized singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions. Such equations can be transformed into Riemann boundary value problems with two unknown functions on two parallel straight lines via Fourier transformation. The general solutions and the conditions of solvability are obtained by means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation. This paper will be of great significance for the study of improving and developing complex analysis, integral equation and boundary value problem. Therefore, the classic Riemann boundary value problem is extended further.