Spectral relationships for the integral equation with Macdonald kernel and contact problem

摘要

A spectral relationship is set up, using the generalized potential theory method for an integral operator generated by a symmetric difference kernel in the form of a Macdonald function in the semi-infinite intervals (−∞,−aj), (aj,∞), j=1,2,…,l, that contain the spheriodal wave functions. On the basis of the results obtained, a closed form solution of the axi-symmetric contact problem is constructed for a finite system of impressing stamps of angular form in a plane into a half-space occupying the domain −∞