Theory of integral equations for axisymmetric scattering by a disk

A theory of integral equations for radial currents in the axisymmetric problem of scattering by a disk is constructed. The theory relies on the extraction of the principal part of a continuously invertible operator and on the proof of its positive definiteness. Existences and uniqueness theorems are obtained for the problem. An orthonormal basis is constructed for the energy space of the positive definite operator. Each element of the basis on the boundary behaves in the same manner as the unknown function. The structure of the matrix of the integral operator in this basis is studied. It is found that the principal part has an identity matrix, while the matrix of the next operator is tridiagonal.