Journal of Operator Theory

Volume 47, Issue 2, Spring 2002 pp. 325-341.

On a class of non-self-adjoint quadratic matrix operator pencils arising in elasticity theory

Authors: Vadim Adamjan (1), Vjacheslav Pivovarchik (2), and Christiane Tretter (3)
Author institution: (1) Department of Theoretical Physics, University of Odessa, Ul. Dvorjanskaja 2, 650026 Odessa, Ukraine
(2) Department of Higher Mathematics, Odessa State Academy of Civil Engineering and Architecture, Ul. Didrikhsona 4, 650028 Odessa, Ukraine
(3) Department of Mathematics, University of Bremen, Bibliothekstr. 1, D--28359 Bremen, Germany

Summary: This paper deals with a class of non-self-adjoint quadratic pencils of block operator matrices. The main results concern the structure and location of the spectrum and theorems about the minimality, completeness and basis properties of the eigenvectors and associated vectors corresponding to certain parts of the spectrum. Finally, an application to the problem of vibrations of a rotating beam is given.

Keywords: quadratic operator pencil, completeness of basis of eigenvectors

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