Solvability theory of convolution singular integral equations via Riemann–Hilbert approach

Abstract

In this paper, we study the solvability for some classes of singular integral equations of convolution type with discontinuous property in class {0}. Though such equations can be solved by using the classical Bekya regularization method, we are to give a new sectionally jumping method, that is, they may be reduced to boundary value problems of holomorphic functions which can be systematically solved and easily discussed. We obtain the general solutions and the conditions of their solvability. Thus, this paper generalizes the classical theory of integral equations.