ON A CLASS OF NON-SELF-ADJOINT QUADRATIC MATRIX OPERATOR PENCILS ARISING IN ELASTICITY THEORY

Abstract

Abstract. This paper deals with a class of non-self-adjoint quadratic pen-cils 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.