Spectral relationships for the integral operators generated by a kernel in the form of a weber-son in integral, and their application to contact problems

Abstract Generalized potential theory methods are used to re-establish the spectral relationship /1/ for the integral operators generated by a symmetric kernel in the form of the Weber-Sonin integral in the finite interval (0, α), the kernel containing Jacobi polynomials. Spectral relations are also established for the integral operator generated by the same kernel in the semi-infinite interval (α,∞), and other allied relationships. The latter are used to construct a closed solution of the axisymmetric contact problem of impressing a stamp of annular form in a plane, with an infinite outer radius, into a half-space, the deformation of which obeys a power law. The monographs /2, 3/ give a large number of various spectral relationships in terms of orthogonal polynomials for the integral operators frequently encountered in mathematical physics, and describe a method of orthogonal polynomials based on them. They also show numerous applications of the method to the contact and mixed problems of the theory of elasticity. Spectral relations and their applications to the mixed problems are also given in /4, 5/. These papers are discussed in detail in /6/.