Spectral relationships for the integral equation with Macdonald kernel and contact problem (Q1855112)

Singular integral equations with difference kernels are widely applied in the study of physical phenomena, population genetics, mechanics, and contact problems in the theory of elasticity, etc. In this paper the author establishes a spectral relationship for an integral operator generated by a symmetric difference kernel in the form of Macdonald function. On the basis of the obtained results, a solution is constructed for the integral equation of the contact problem for the impression of a system of stamp with half-plane bases into a half-space being deformed in a power-law form in the formulation. The formulation of the problem, the potential theory method, and the method of solution are discussed.