Book:Erich Müller-Pfeiffer/Spectral Theory of Ordinary Differential Operators
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Erich Müller-Pfeiffer: Spectral Theory of Ordinary Differential Operators
Published $\text {1981}$, Ellis Horwood
- ISBN 0-85312-189-3
Subject Matter
Contents
- Foreword
- Author's Preface
- Chapter 1 - FUNDAMENTAL CONCEPTS
- Operators in Hilbert Space
- Spectral Theorem and Spectrum
- Sesquilinear Forms
- Courant's Variational Principle
- Decomposition of Operators
- Deficiency Indices
- Chapter 2 - THE ESSENTIAL SPECTRUM
- The Adjoint Operator
- Differential Operators with Constant Coefficients: Self-adjoint and Essentially Self-adjoint Operators
- Invariance of the Essential Spectrum under Perturbations
- Localization of the Essential Spectrum
- Relatively Compact Perturbations
- Existence of Isolated Eigenvalues
- The Euler Differential Operator
- Chapter 3 - DISCRETE SPECTRA
- Sufficient Conditions
- Necessary and Sufficient Conditions
- Second-Order Differential Operators
- The Infimum of the Spectrum of Periodic Differential Operators
- Chapter 4 - CONTINUOUS SPECTRA
- Self-adjoint Operators and Boundary Conditions
- Non-Existence of Eigenvalues
- The Friedrichs Extension
- Chapter 5 - STURM-LIOUVILLE OPERATORS
- Oscillation and the Spectrum
- Non-Existence of Eigenvalues
- Special Cases
- Chapter 6 - OSCILLATION CRITERIA
- Kneser-Type Conditions
- Special Cases
- Integral Conditions
- Special Cases
- The Sturm-Liouville Equation
- Appendix
- References
- Index