Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation

Abstract

Communicated by A. KirschWe considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein-Gordon differential equation with a nonlinear spectral parameter-dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering function S. /; in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson-type formula, was obtained. Copyright