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Non-Self-Adjoint Boundary Eigenvalue Problems

Autor: Reinhard Mennicken, Manfred Moller

Język:

Oprawa: Twarda

Wydawca: North-Holland

Dostępność: Dostępna u dostawcy

Wysyłamy za 10-18 dni

732.74 zł

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first...

Informacje o książce

Autor

Reinhard Mennicken, Manfred Moller

Język

Angielski

Oprawa

Książka - Twarda

Data wydania

2003

strony

518

EAN

9780444514479

ISBN

0444514473

Enbook ID

04611192

Wydawca

North-Holland

Waga

900

Wymiary

174 x 243 x 27

Pełny opis

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-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 n-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 and 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 of this title are as mentioned below. It includes expansion theorems for ordinary differential equations. It discusses applications to problems from physics and engineering. It provides thorough investigation of asymptotic fundamental matrices and systems. It also provides a comprehensive treatment. It uses the contour integral method. It represents the problems as bounded operators. It investigates canonical systems of eigen- and associated vectors for operator functions.

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