Spectral relationships for the integral equation with Macdonald kernel andcontact problem

A spectral relationship is set up, using the generalized potential theory m ethod for an integral operator generated by a symmetric difference kernel i n the form of a Macdonald function in the semi-infinite intervals (-infinit y, -a(j)), (a(j), infinity), j = 1, 2,..., l, that contain the spheriodal w ave 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 t he domain -infinity < x < infinity, \y\ greater than or equal to a(j), z = 0, j = 1, 2,..., l. Many different cases are discussed in this work. (C) 20 02 Elsevier Science Inc. All rights reserved.