MATH 8367 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; 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, Fredholm Theory.

Credits

3

Prerequisite

Consent of instructor

Schedule Type

Lecture

Grading Basis

Standard Letter (A-F)

Offered

As scheduled