A new efficient method for some classes of non-normal type singular
integral equations with convolution
Abstract
In this work, we deal with the existence and uniqueness of solutions for
some classes of singular integral equations with convolution in the case
of non-normal type. To obtain the conditions of Noethericity, we
establish the regularity theory of solvability for the equations. By
means of the theory of Fourier analysis, we transform such equations
into Riemann boundary value problems. The analytic solutions and the
conditions of solvability are obtained in class
$\{0\}$. In particular, we discuss the
asymptotic property of solutions at nodes. Therefore, our work
generalizes ones in Refs.[1,2,4,5,11,12,15] and improves the
theories of integral equations and the classical Riemann boundary value
problems.