Edition |
1st ed. |
Description |
1 online resource (xviii, 500 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
Series |
North-Holland mathematics studies, 0304-0208 ; 192 |
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North-Holland mathematics studies ; 192. 0304-0208
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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.
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Nonselfadjoint operators.
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Eigenvalues.
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Differential equations.
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Problèmes aux limites.
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Opérateurs non auto-adjoints.
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Valeurs propres.
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Équations différentielles.
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MATHEMATICS -- Differential Equations -- General.
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Boundary value problems
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Differential equations
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Eigenvalues
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Nonselfadjoint operators
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Randwertproblem
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Problemas de contorno.
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Operadores.
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Espaços de sobolev.
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Equações diferenciais.
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Added Author |
Möller, Manfred (Mathematician)
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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 |
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0444514473 |
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9780080537733 |
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0080537731 |
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1281048747 |
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9781281048745 |
Standard No. |
AU@ 000048129756 |
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CHNEW 001006609 |
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DEBBG BV036962340 |
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DEBBG BV039830208 |
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DEBBG BV042317340 |
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DEBSZ 276782909 |
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DEBSZ 482355611 |
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NZ1 12433593 |
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NZ1 15192897 |
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AU@ 000059689025 |
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