Translations of Mathematical Monographs 1988; 250 pp; hardcover Volume: 71 ISBN10: 0821845233 ISBN13: 9780821845233 List Price: US$105 Member Price: US$84 Order Code: MMONO/71
 This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Kreĭn and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space. Table of Contents  Operators with compact resolvent which are close to being normal
 Keldysh pencils
 Factorization of pencils
 Selfadjoint pencils
