Perturbation of eigenvalues of the Klein–Gordon operators

Abstract

We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein–Gordon type Hamiltonian operators. We first study operators of the form JG, where J, G are selfadjoint operators on a Hilbert space, $$J = J^* = J^{-1}$$ and G is positive definite and then we apply these results to obtain bounds of the Klein–Gordon eigenvalues under the change of the electrostatic potential. The developed general theory allows applications to some other instances, as e.g. the Sturm–Liouville problems with indefinite weight.