Krein's method for solving the integral equation of the first kind With logarithmic kernel

Abstract

Consider the Fredholm's integral equation of the first kind with logarithmic kernel K(IXI) = (- In Ixl. The aim of this paper is to establish the equivalence of Krein's method of solving the equation with the following methods of solution: method of potential theory, method of singular integral equations, method of orthogonal polynomials and method of Fourier transformation.