TY  - BOOK
AU  - Mennicken,Reinhard
AU  - M�oller,Manfred
TI  - Non-self-adjoint boundary eigenvalue problems
T2  - North-Holland mathematics studies,
SN  - 9780444514479
AV  - QA379 .M45 2003eb
U1  - 515/.35 22
PY  - 2003///
CY  - Amsterdam, Boston
PB  - North-Holland
KW  - Boundary value problems
KW  - Nonselfadjoint operators
KW  - Eigenvalues
KW  - Differential equations
KW  - Probl�emes aux limites
KW  - Op�erateurs non auto-adjoints
KW  - Valeurs propres
KW  - �Equations diff�erentielles
KW  - Problemas de contorno
KW  - larpcal
KW  - Operadores
KW  - Espa�cos de sobolev
KW  - Equa�c�oes diferenciais
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references (p. 475-495) and index
N2  - 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
UR  - http://www.sciencedirect.com/science/book/9780444514479
UR  - http://www.sciencedirect.com/science/publication?issn=03040208&volume=192
ER  -