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

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Erich Müller-Pfeiffer: Spectral Theory of Ordinary Differential Operators

Published $1981$, 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