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

2018/01/01 by Olga Boyko, Boyko, Olga, O. V. Martynyuk +3
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1801.00463

openalex publication_date 2018/01/01 · openalex created_date 2022/08/07 · openalex updated_date 2026/07/28

Abstract

The spectrum of a selfadjoint quadratic operator pencil of the form\n\λ²M-\λ G-A is investigated where M\≥ 0, G\≥ 0 are bounded\noperators and A is selfadjoint bounded below is investigated. It is shown\nthat in the case of rank one operator G the eigenvalues of such a pencil are\nof two types. The eigenvalues of one of these types are independent of the\noperator G. Location of the eigenvalues of both types is described. Examples\nfor the case of the Sturm-Liouville operators A are given.\n

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