MATH 8367 Advanced 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, Stone-Weierstrass Theorem, Riesz Theorem, compact operators, Hilbert spaces, linear operators on Hilbert spaces, eigenvalues and eigenvectors of operators, spectral theorem and functional calculus for compact normal operators, unbounded self-adjoint and symmetric operators and their spectral decomposition, Cayley transform, unbounded normal operators and the spectral theorem, and Fredholm Theory.
Prerequisite
Consent of instructor.
Offered
As scheduled