Abstract
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 (−∞,−
a
j
), (
a
j
,∞),
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 −∞<
x<∞, |
y|⩾
a
j
,
z=0,
j=1,2,…,
l. Many different cases are discussed in this work.