Non-Self-Adjoint Boundary Eigenvalue ProblemsElsevier, 2003. 6. 26. - 518페이지 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. 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.
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목차
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Chapter II First order systems of ordinary differential equations | 53 |
Chapter III Boundary eigenvalue problems for first order systems | 101 |
Chapter IV Birkhoff regular and Stone regular boundary eigenvalue problems | 129 |
Chapter V Expansion theorems for regular boundary eigenvalue problems for first order systems | 203 |
Chapter VI nth order differential equations | 249 |
Chapter VII Regular boundary eigenvalue problems for nth order equations | 279 |
Chapter VIII The differential equation KηλHη | 321 |
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자주 나오는 단어 및 구문
according adjoint apply assertion associated functions associated vectors assume assumptions asymptotic Banach space belongs biorthogonal Birkhoff regular block boundary conditions boundary eigenvalue problem bounded calculate called canonical chapter characteristic choose coefficients compact complete components consider constant continuous converges Corollary corresponding CSEAV CSRF defined definition depend determinant diagonal differential equations differential operators eigenvectors elements equivalent estimate example expansion follows fundamental matrix fundamental system given Hence holds holomorphic identity immediately implies independent infer integral interval invertible Lemma linear Math matrix function multiplicity obtain Obviously operator function points polynomial Proof properties Proposition proves Remark representation respect root functions Russian satisfied shows solution subset sufficiently Suppose Theorem tions transformation u e o unique write yields
도서 문헌정보
| 제목 | Non-Self-Adjoint Boundary Eigenvalue Problems |
| 저자 | R. Mennicken, M. Möller |
| 발행인 | Elsevier, 2003 |
| ISBN | 0080537731, 9780080537733 |
| 길이 | 518페이지 |
| 서지정보 내보내기 | BiBTeX EndNote RefMan |