engleski

Perturbation of eigenvalues of the Klein-Gordon operators

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.

Klein-Gordon equation ; Hamiltonian ; Perturbation theory ; Spectral operators

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