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Department:
MATH
Course Number:
6338
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every spring and some summer semesters
Topics include L^p, Banach and Hilbert spaces, basic functional analysis.
Prerequisites:
Math 6337 or consent of the school
Course Text:
At the level of Folland, Real Analysis
Topic Outline:
- 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.