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Department:
MATH
Course Number:
7338
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every even fall semester
Topics include the Hahn-Banach theorems, the Baire Category theorem and its consequences, duality in Banach spaces, locally convex spaces, additional topics.
Course Text:
At the level of Conway: A Course in Functional Analysis, 2nd edition, Springer-Verlag
Topic Outline:
- Normed, Banach, and Hilbert spaces
- Operators on Banach and Hilbert spaces, linear functionals, the Riesz Representation Theorem
- Hahn-Banach theorem, Baire Category theorem, open mappings, theorem, closed graph theorem, and the uniform boundedness principle
- Locally convex spaces, weak topologies, duality, Alaoglu's theorem, Krein-Milman theorem
- Other applicatins and topics at the discretion of the instructor, such as
- Distributions
- The Fourier transform
- Sturm-Liouville systems
- Sobolev spaces
- Banach algebras
- Compact operators on a Banach space, Riesz functional calculus
- Fixed point theorems