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Author Mennicken, Reinhard.

Title Non-self-adjoint boundary eigenvalue problems / Reinhard Mennicken and Manfred Möller.

Imprint Amsterdam ; Boston : North-Holland, 2003.

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Location Call No. OPAC Message Status
 Axe Elsevier ScienceDirect Ebook  Electronic Book    ---  Available
Edition 1st ed.
Description 1 online resource (xviii, 500 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series North-Holland mathematics studies, 0304-0208 ; 192
North-Holland mathematics studies ; 192. 0304-0208
Summary This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and <IT>n</IT>-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every <IT>n</IT>-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: & bull; Expansion Theorems for Ordinary Differential Equations & bull; Discusses Applications to Problems from Physics and Engineering & bull; Thorough Investigation of Asymptotic Fundamental Matrices and Systems & bull; Provides a Comprehensive Treatment & bull; Uses the Contour Integral Method & bull; Represents the Problems as Bounded Operators & bull; Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions.
Bibliography Includes bibliographical references (pages 475-495) and index.
Note Print version record.
Contents Front Cover; Non-Self-Adjoint Boundary Eigenvalue Problems; Copyright Page; Contents; Introduction; Chapter I. Operator functions in Banach spaces; Chapter II. First order systems of ordinary differential equations; Chapter III. Boundary eigenvalue problems for first order systems; Chapter IV. Birkhoff regular and Stone regular boundary eigenvalue problems; Chapter V. Expansion theorems for regular boundary eigenvalue problems for first order systems; Chapter VI. n-th order differential equations; Chapter VII. Regular boundary eigenvalue problems for n-th order equations.
Subject Boundary value problems.
Nonselfadjoint operators.
Eigenvalues.
Differential equations.
Problèmes aux limites.
Opérateurs non auto-adjoints.
Valeurs propres.
Équations différentielles.
MATHEMATICS -- Differential Equations -- General.
Boundary value problems
Differential equations
Eigenvalues
Nonselfadjoint operators
Randwertproblem
Problemas de contorno.
Operadores.
Espaços de sobolev.
Equações diferenciais.
Added Author Möller, Manfred (Mathematician)
Other Form: Print version: Mennicken, Reinhard. Non-self-adjoint boundary eigenvalue problems. 1st ed. Amsterdam ; Boston : North-Holland, 2003 0444514473 9780444514479 (DLC) 2003054700 (OCoLC)52334745
ISBN 9780444514479
0444514473
9780080537733
0080537731
1281048747
9781281048745
Standard No. AU@ 000048129756
CHNEW 001006609
DEBBG BV036962340
DEBBG BV039830208
DEBBG BV042317340
DEBSZ 276782909
DEBSZ 482355611
NZ1 12433593
NZ1 15192897
AU@ 000059689025

 
    
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