Introduction to the spectral theory of polynomial operator pencils
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Bibliographic Information
Introduction to the spectral theory of polynomial operator pencils
（Translations of mathematical monographs, v. 71）
American Mathematical Society, c1988
- Other Title
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Vvedenie v spektralʹnui︠u︡ teorii︠u︡ polinomialʹnykh operatornykh puchkov
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
MAR||77||1(M)88069673
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:515.7/M3422070109205
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Translation of: Vvedenie v spektralʹnui︠u︡ teorii︠u︡ polinomialʹnykh operatornykh puchkov
Includes index
Description and Table of Contents
Description
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.
Table of Contents
Operators with compact resolvent which are close to being normal Keldysh pencils Factorization of pencils Selfadjoint pencils.
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