Scattering Theory for 0-Perturbed $\mathcal{P}\mathcal{T}$ -Symmetric Operators

Abstract

The aim of the present work is to develop the scattering theory for 0-perturbed $\mathcal{P}\mathcal{T}$ -symmetric operators by using the Lax–Phillips method. The presence of a stable $\mathcal{C}$ -symmetry leading to the property of selfadjointness (with proper choice of the inner product) for these PTPT -symmetric operators is described in terms of the corresponding $\mathcal{C}$ -matrix (scattering matrix).