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arXiv · 1807.11612

Perturbation of eigenvalues of the Klein-Gordon operators

Ivica Nakić·Krešimir Veselić
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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.

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Ivica Nakić, Krešimir Veselić. 2018-07-31. Perturbation of eigenvalues of the Klein-Gordon operators. https://arxiv.org/abs/1807.11612

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