Book:Erich Müller-Pfeiffer/Spectral Theory of Ordinary Differential Operators

Subject Matter

 * Ordinary Differential Equations

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