MATH 7130: Functional Analysis (Spring 2010)

Instructor: Leonard Gross

The course will cover basic topics in functional analysis. The main prerequisites are elementary Hilbert space and Banach space principles, as represented in chapters four and five of Rudin's book Real and Complex Analysis. We will follow a set of notes which will be distributed.

Topics to be covered are:

1. Topological vector spaces.
2. Banach algebras
3. The spectral theorem for bounded and unbounded self-adjoint operators. Application to PDE's.
4. Compact operators
5. Semigroups of operators.