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

**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].
**Compact operators**: the Fredholm-Riesz-Schauder theory,
elements of spectral theory, application to PDEs.
**Hilbert spaces**: the projection theorem and projection operators,
orthonormal sets.
**Operators and spectral theory in a Hilbert space**: self-adjoint
operators, eigenvalue problems for differential and integral equations.

Books:
Avner Friedman, "Foundations of Modern Analysis", Dover Publications,
New York, 1982.