# $\mathcal C$-symmetric Hamiltonian systems with almost constant coefficients

### Horst Behncke

Universität Osnabrück, Germany### Don B. Hinton

University of Tennessee, Knoxville, USA

## Abstract

We consider a $\mathcal C$-Symmetric Hamiltonian System of differential equations on a half interval or the real line. We determine the spectrum and construct the resolvent for the system. The essential spectrum is found to be a subset of an algebraic curve $\Sigma$ defined by a characteristic polynomial for the system. The results are first proved for a constant coefficient system and then for an almost constant coefficient system. The results are applied to a number of examples including the complex hydrogen atomand the complex relativistic electron.

## Cite this article

Horst Behncke, Don B. Hinton, $\mathcal C$-symmetric Hamiltonian systems with almost constant coefficients. J. Spectr. Theory 9 (2019), no. 2, pp. 513–546

DOI 10.4171/JST/254