ON THE EIGENVALUES OF THE ELECTROSTATIC INTEGRAL OPERATOR .2.

A fundamental result in scattering and potential theory in R3 states that the spectrum of the electrostatic integral operator lies in the interval [-1,1). In the case of a sphere and a prolate spheroid, it is known that the spectrum of the operator lies in the interval [-1,0]. A fundamental question arises whether the spectrum of the operator always lies in this interval, or whether there exists a smooth surface for which the electrostatic integral operator has a positive eigenvalue. In this paper, this question is answered. A surface is produced whereby the underlying integral operator has a positive eigenvalue. (C) 1994 Academic Press. Inc.