On elements of the Lax-Phillips scattering scheme for PT-symmetric operators

TL;DR

This paper explores the application of Lax-Phillips scattering methods to PT-symmetric operators, focusing on extensions of symmetric operators and their potential for analyzing 0-perturbed cases in a Hilbert space.

Contribution

It introduces a framework for applying Lax-Phillips scattering theory to PT-symmetric operators and examines their extensions in detail.

Findings

PT-symmetric operators can be effectively analyzed using Lax-Phillips methods.

Extensions of symmetric operators are characterized within the PT-symmetric framework.

Application to 0-perturbed operators demonstrates practical utility.

Abstract

Generalized PT-symmetric operators acting an a Hilbert space $\mathfrak{H}$ are defined and investigated. The case of PT-symmetric extensions of a symmetric operator $S$ is investigated in detail. The possible application of the Lax-Phillips scattering methods to the investigation of PT-symmetric operators is illustrated by considering the case of 0-perturbed operators.