Instructor: Dr. Gábor ELEK
Text: handout (the notes of the lecturer) (and M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. I.: Functional Analysis. Academic Press, New York and London 1972)
Prerequisite: Advanced calculus, basic linear algebra. Some introduction to real analysis is helpful.
The course material consists of three major parts. The first is a short introduction to the basic topology and real analysis we need:
Basic real analysis
-- Compact metric spaces
-- Complete spaces
-- A short introduction to measure theory
-- Borel sets
The second part is the classical functional analysis part.
-- Hilbert spaces
-- Dual spaces
-- Banach-Steinhaus and the open mapping theorem
The third part consists of applications of functional analysis in various fields of mathematics:
-- Dynamical systems
-- Invariant measures and ergodicity.