# 7 documents found

Article / Chapter
2014-04-28

### On limit point and limit circle classification for PT symmetric operators

A prominent class of PT-symmetric Hamiltonians is H:= 1/2 p^2 + x^2 (ix)^N, for x \in \Gamma$for some nonnegative number N. The associated eigenvalue problem is defined on a contour$\Gamma\$ in a specific area in the complex plane (Stokes wedges), see [3,5]. In this short note we consider the case...
Article / Chapter
2011-08-23

### PT symmetric, hermitian and P-selfadjoint operators related to potentials...

In the recent years a generalization of the harmonic oscillator using a complex deformation was investigated, where epsilon is a real parameter. Here, we will consider the most simple case: even and x real. We will give a complete characterization of three different classes of operators associated with...
Article / Chapter
2009-11-11

### On domains of PT symmetric operators related to −y′′(x) + (−1)nx2ny(x)

In the recent years a generalization of Hermiticity was investigated using a complex deformation H = p2 + x2(ix)? of the harmonic oscillator Hamiltonian, where ? is a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum....
Article / Chapter
2008-04-16

### Spectral points of definite type and type π for linear operators and relations...

Spectral points of type \pi_+ and type \pi_− for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. It turns out that these spectral points are stable under compact perturbations and perturbations small in the gap metric.
Article / Chapter
2008-01-30

### Small perturbation of selfadjoint and unitary operators in Krein spaces

We investigate the behaviour of the spectrum of selfadjoint operators in Krein spaces under perturbations with uniformly dissipative operators. Moreover we consider the closely related problem of the perturbation of unitary operators with uniformly bi-expansive. The obtained perturbation results give...
Article / Chapter