This introduction adresses to M2 students in pure/applied mathematics. We present the basic tools in spectral analysis and provide examples from the Schrödinger operator theory. Notions of analysis, the definitions and basic properties of Banach and Hilbert spaces are required.
- 1. What is a Spectrum ?
- 2. Operators on Banach and Hilbert spaces
- 3. Operators as quadratic forms
- 4. Spectrum and resolvent
- 5. Spectral theory of compact operators
- 6. The spectral theorem for selfadjoint operators
- 7. Perturbation theory
- 8. Variational methods
The course is inspired to the
Lecture Notes by K. Pankrashkin and S. Nonnenmacher.
The interested reader will find an extensive bibliography therein.
