On spectra of quadratic operator pencils with rank one gyroscopic linear part
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...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2018-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3822.pdf |
| _version_ | 1818202363173797888 |
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| author | Olga Boyko Olga Martynyuk Vyacheslav Pivovarchik |
| author_facet | Olga Boyko Olga Martynyuk Vyacheslav Pivovarchik |
| author_sort | Olga Boyko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T03:08:15Z |
| format | Article |
| id | doaj.art-1bbab39249be432c9f01646c382d0edd |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-12T03:08:15Z |
| publishDate | 2018-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-1bbab39249be432c9f01646c382d0edd2022-12-22T00:40:28ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01384483500https://doi.org/10.7494/OpMath.2018.38.4.4833822On spectra of quadratic operator pencils with rank one gyroscopic linear partOlga Boyko0Olga Martynyuk1Vyacheslav Pivovarchik2South-Ukrainian National Pedagogical University, Staroportofrankovskaya Str. 26, Odesa, 65020, UkraineSouth-Ukrainian National Pedagogical University, Staroportofrankovskaya Str. 26, Odesa, 65020, UkraineSouth-Ukrainian National Pedagogical University, Staroportofrankovskaya Str. 26, Odesa, 65020, UkraineThe 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.http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3822.pdfquadratic operator pencilgyroscopic forceeigenvaluesalgebraic multiplicity |
| spellingShingle | Olga Boyko Olga Martynyuk Vyacheslav Pivovarchik On spectra of quadratic operator pencils with rank one gyroscopic linear part Opuscula Mathematica quadratic operator pencil gyroscopic force eigenvalues algebraic multiplicity |
| title | On spectra of quadratic operator pencils with rank one gyroscopic linear part |
| title_full | On spectra of quadratic operator pencils with rank one gyroscopic linear part |
| title_fullStr | On spectra of quadratic operator pencils with rank one gyroscopic linear part |
| title_full_unstemmed | On spectra of quadratic operator pencils with rank one gyroscopic linear part |
| title_short | On spectra of quadratic operator pencils with rank one gyroscopic linear part |
| title_sort | on spectra of quadratic operator pencils with rank one gyroscopic linear part |
| topic | quadratic operator pencil gyroscopic force eigenvalues algebraic multiplicity |
| url | http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3822.pdf |
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