On the Lax–Phillips scattering matrix of the abstract wave equation

Abstract

We study the dependence of singularities of scattering matrices of the abstract wave equation on the choice of asymptotically equivalent outgoing/incoming subspaces. We apply the obtained results to the radial wave equation with nonlocal potential. In the latter case, the concept of associated inner function—introduced by Douglas, Shapiro, and Shields in 1970—plays an essential role.