1. Basic theory of unbounded operators
(adjoints, spectrum, Fredholm operators, normal eigenvalues [the discrete spectrum], operators in the Hilbert space: symmetric, normal, self-adjoint)
2. Essential spectra and the Weyl theorem
3. Limiting absorption principle for the Schroedinger operators
4. The Keldysh theory of characteristic roots
5. Virtual levels and virtual states
The main references will be:
1. T. Kato, Perturbation theory for linear operators
2. N. Boussaid and A. Comech, Nonlinear Dirac equation
3. D. Yafaev, Mathematical scattering theory
4. D. Edmunds and W. Evans, Spectral theory and differential operators
Prerequisites: none