7 documents found

Article / Chapter
All rights reserved
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
All rights reserved
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
All rights reserved
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
All rights reserved
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
All rights reserved
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
All rights reserved
2007-12-14

Compact and finite rank perturbations of linear relations in Hilbert spaces

Abstract. For closed linear operators or relations A and B acting between Hilbert spaces H and K the concepts of compact and finite rank perturbations are introduced with the help of the orthogonal projections PA and PB in H©K onto A and B. Various equivalent characterizations for such perturbations...
Article / Chapter
All rights reserved
2007-12-10

On domains of powers of linear operators and finite rank perturbations

Let S and T be linear operators in a linear space such that S T. In this note an estimate for the codimension of domSn in domTn in terms of the codimension of domS in domT is obtained. An immediate consequence is that for any polynomial p the operator p(S) is a finite-dimensional restriction of the...