Introduction to the Spectral Theory of Polynomial Operator Pencils (Translations of Mathematical Monographs) (English and Russian Edition) - Hardcover

Markus, A. S.

Hardcover

ISBN 10: 0821845233 ISBN 13: 9780821845233

Publisher: Amer Mathematical Society, 1988

Synopsis

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. Krein 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.

About this title

Language Notes

Text: English, Russian (translation)

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 1988
• Language: English
• ISBN 10: 0821845233
• ISBN 13: 9780821845233
• Binding: Hardcover
• Number of pages: 250