"Foundations of Modern Analysis 2". School of Mathematical Sciences. (Ya. Yakubov)

1. Foundations of functional analysis in Banach spaces: finite and infinite dimensional normed linear spaces, linear transformations, the open-mapping theorem and the closed-graph theorem, application to PDEs, the Hahn-Banach theorem, conjugate spaces and reflexive spaces, adjoint operators, the conjugates of L^p and C[0,1].
2. Compact operators: the Fredholm-Riesz-Schauder theory, elements of spectral theory, application to PDEs.
3. Hilbert spaces: the projection theorem and projection operators, orthonormal sets.
4. Operators and spectral theory in a Hilbert space: self-adjoint operators, eigenvalue problems for differential and integral equations.