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Introduction to the Spectral Theory of Polynomial Operator Pencils
 
Introduction to the Spectral Theory of Polynomial Operator Pencils
eBook ISBN:  978-1-4704-4485-3
Product Code:  MMONO/71.E
List Price: $155.00
AMS Member Price: $146.32
Introduction to the Spectral Theory of Polynomial Operator Pencils
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Introduction to the Spectral Theory of Polynomial Operator Pencils
eBook ISBN:  978-1-4704-4485-3
Product Code:  MMONO/71.E
List Price: $155.00
AMS Member Price: $146.32
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 711988; 250 pp
    MSC: Primary 47

    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
     
     
    • Chapters
    • Introduction
    • Operators with compact resolvent which are close to being normal
    • Keldysh pencils
    • Factorization of pencils
    • Selfadjoint pencils
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 711988; 250 pp
MSC: Primary 47

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.

  • Chapters
  • Introduction
  • Operators with compact resolvent which are close to being normal
  • Keldysh pencils
  • Factorization of pencils
  • Selfadjoint pencils
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.