MATH 6367 Functional Analysis
This course provides an introduction to methods and applications of functional analysis. Topics include: topological vector spaces; locally convex spaces (Hahn-Banach Theorem, weak topology, dual pairs); normed spaces; theory of distributions (space of test functions, convolution, Fourier transform; Sobolev spaces); Banach spaces (Uniform Boundedness Principle, Open Mapping Theorem, Closed Graph Theorem and applications, Banach-Alaoglus Theorem, Krein-Milman Theorem); C(X) as a Banach space (Stone-Weierstrass Theorem, Riesz Theorem, compact operators); Hilbert spaces; linear operators on Hilbert spaces; eigenvalues and eigenvectors of operators.
Prerequisite
MATH 3372 Real Analysis I with a grade of ?C? or higher or consent of instructor.
Offered
As scheduled