Solvability of singular integro-differential equations via Riemann–Hilbert problem

Abstract

The article is to study singular integro-differential equations involving convolutional operators and Cauchy integral operators via Riemann–Hilbert problem. To do this, we adopt a new approach through Fourier transform on L2 subspace which is Hölder-continuous with a certain decay at infinity. The Fourier transform converts the equations into a Riemann–Hilbert problem with Hölder-continuous coefficients and with nodal points, which allows us to construct the general solutions.