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arXiv · 1801.00463

On spectra of quadratic operator pencils with rank one gyroscopic linear part

Olga Boyko·Olga Martynyuk·Vyacheslav Pivovarchik
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Abstract

The spectrum of a selfadjoint quadratic operator pencil of the form $\lambda^2M-\lambda G-A$ is investigated where $M\geq 0$, $G\geq 0$ are bounded operators and $A$ is selfadjoint bounded below is investigated. It is shown that in the case of rank one operator $G$ the eigenvalues of such a pencil are of two types. The eigenvalues of one of these types are independent of the operator $G$. Location of the eigenvalues of both types is described. Examples for the case of the Sturm-Liouville operators $A$ are given.

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Olga Boyko, Olga Martynyuk, Vyacheslav Pivovarchik. 2018-01-01. On spectra of quadratic operator pencils with rank one gyroscopic linear part. https://arxiv.org/abs/1801.00463

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