ABSTRACT
Ralph Kleinman who introduced the author to integral equation methods in scattering theory and started him to view wave propagation as a discipline in its own right and not simply an area in which he could use his latest integral operator. In their only paper together, Raph and the author showed how to modify the kernel of the double layer potential for the Helmholtz equation in a domain independent manner such that the spectral radius of the operator was less than one for sufficiently small values of the wave number. This idea of modifying the kernel of the integral equations of scattering theory was subsequently pursued by Ralph and Gary Roach in order to eliminate the “critical values” of the standard integral equation formulation of the exterior Dirichet and Neumann problem for the Helmholtz equation.
