Topics include L^p, Banach and Hilbert spaces, basic functional analysis.
MATH 4318 or consent of the school
At the level of Folland, Real Analysis
- Basics of measure theory
- L^p spaces: Completeness, Riesz representation and the dual of L^p, Hölder's, Jensen's, and Minkowski's inequalities.
- Topological spaces, normed vectors spaces, compact spaces and the Tychonoff theorem. Linear functionals, Banach and Hilbert spaces, orthonormal bases and orthogonal projections in Hilbert spaces.
- Basic theorems of functional analysis, including the Hahn-Banach, Baire Category, and open mapping theorems and the uniform boundedness principle.