Functional analysis

Lecturer: Olavi Nevanlinna (Jan 2015 - Apr 2015), Ville Turunen (Sep 2015 - Oct 2015)
Teaching assistant: Armando W. Gutiérrez

Content:

norms, seminorms, inner products
bounded linear operators
Riesz compact theorem, uniform boundedness principle, open mapping and closed graph theorems
Hahn-Banach theorem
duality and spectral theory
Gelfand’s spectral theorem
orthogonality, orthonormal bases
Riesz representation theorem
diagonalization of compact self-adjoint operators
Hilbert-Schmidt spectral theorem
singular value decomposition

Study material: