Details

Autor(en) / Beteiligte

• Mennicken, Reinhard
• Möller, Manfred,

Titel

Non-self-adjoint boundary eigenvalue problems [electronic resource]

Auflage

1st ed

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and index.
• Cover; Contents; Introduction; Chapter I. Operator functions in Banach spaces; 1.1. Banach spaces; 1.2. Holomorphic vector valued functions; 1.3. The inverse of a Fredholm operator valued function; 1.4. Root functions of holomorphic operator functions; 1.5. Representation of the principal part of a finitely meromorphic oper- ator function; 1.6. Eigenvectors and associated vectors; 1.7. Semi-simple eigenvalues; 1.8. Local factorizations; 1.9. The completion of biorthogonal systems of root functions; 1.10. The operator function A + λB; 1.11. Abstract boundary eigenvalue operator functions
• 3.3. The adjoint boundary eigenvalue problem3.4. The adjoint boundary eigenvalue problem in parametrized form; 3.5. Two-point boundary eigenvalue problems in (Lp (a, b) )n; 3.6. Notes; Chapter IV. Birkhoff regular and Stone regular boundary eigenvalue problems; 4.1. Definitions and basic results; 4.2. Examples of Birkhoff regular problems; 4.3. Estimates of the characteristic determinant; 4.4. Estimates of the Green's matrix; 4.5. A special case of the Hilbert transform; 4.6. Improved estimates of the Green's matrix; 4.7. Uniform estimates of the Green's matrix; 4.8. Notes
• Chapter V. Expansion theorems for regular boundary eigenvalue problems for first order systems5.1. First order systems which are linear in the eigenvalue parameter; 5.2. Birkhoff regular first order systems; 5.3. Expansion theorems for Birkhoff regular problems; 5.4. Examples for expansions in eigenfunctions and associated functions; 5.5. Stone regular boundary eigenvalue problems; 5.6. Expansion theorems for Stone regular problems; 5.7. Improved expansion theorems for Stone regular problems; 5.8. Notes; Chapter VI. n-th order differential equations; 6.1. Differential equations and systems
• 6.2. Boundary conditions6.3. The boundary eigenvalue operator function; 6.4. The inverse of the boundary eigenvalue operator function; 6.5. The adjoint of the boundary eigenvalue problem; 6.6. The adjoint boundary eigenvalue problem in parametrized form; 6.7. Two-point boundary eigenvalue problems in Lp (a, b); 6.8. Notes; Chapter VII. Regular boundary eigenvalue problems for n-th order equations; 7.1. General assumptions; 7.2. Asymptotic linearizations; 7.3. Birkhoff regular problems; 7.4. Expansion theorems for Birkhoff regular n-th order differential equa- tions
• 7.5. An example for a Birkhoff regular problem with X-dependent bound- ary conditions
• 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 orde
• English