Volterra’s equation of the second kind with «incompressible» kernel

Abstract

In the article the singular Volterra’s integral equation of the second kind is considered, which because of the «incompressible» of the kernel classical methods of solutions are not applicable. It is shown that the corresponding homogeneous equation at  1 has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing  . By the Carleman-Vekua method the equation is reduced to Abelequation. The eigenfunctions of the equation are found in an explicit form.