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.

中文翻译：

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Klein-Gordon算子的特征值的摄动

我们证明了光谱和基本光谱的包含定理，以及Klein-Gordon型哈密顿算子的孤立特征值的两边定理。我们首先研究形式为JG的算子，其中J，G是希尔伯特空间上的自伴算子，\（J = J ^ * = J ^ {-1} \）并且G是正定的，然后将这些结果应用于以获得静电势变化下Klein-Gordon特征值的界。发达的一般理论允许将其应用于其他一些情况，例如权重不确定的Sturm-Liouville问题。