Synopsis
Explore the theory of second-order differential operators and their spectra with clear, rigorous guidance. This book builds tools for understanding resolvents, self-adjointness, and representation theorems.
The material develops a precise framework for linear operators like L on real and complex-valued functions, explains how to define domains, and shows how spectra relate to boundary conditions. It also covers perturbation theory and the role of resolvents in forming expansions and representations, with attention to both real and complex potentials.
- How to define operators, domains, and resolvents in a way that makes the spectrum meaningful.
- Techniques for handling limit point and limit circle cases in spectral analysis.
- Approaches to perturbation and how bounded perturbations affect the spectrum and resolvent.
- Foundations of representation theorems and elementary aspects of spectral decomposition.
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Linear Ordinary Differential Operators of the Second Order (Classic Reprint)
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