ON SOLVABILITY OF SINGULAR INTEGRAL-DIFFERENTIAL EQUATIONS WITH CONVOLUTION

In this paper, we study a class of singular integral-different equations of convolution type with Cauchy kernel. By means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation, we transform the equations into the Riemann-Hilbert problems with discontinuous coefficients and obtain the general solutions and conditions of solvability in class {0}. Thus, the result in this paper generalizes the classical theory of integral equations and boundary value problems.