Spectral Theory

Hilbert spaces, unbounded linear operators, symmetric and essentially self-adjoint operators, the Cayley transform and von Neumann's theorem for self-adjoint extensions of symmetric operators, spectrum and resolvent set, analytic Fredholm theorem, spectral theorems for unitary and self-adjoint operators, the Borel functional calculus and Stone's formula, spectral measures, decompositions of the spectrum, Weyl criterion and stability, and the RAGE theorem.