Introduction to Spectral Theory
This is an introductory course to those interested in the aspects of spectral theory and its applications. It may be of interest to those who work in PDE, Math-Phys, Analytic Number Theory and Analysis on Manifolds.
I begin with a review of the basics of Hilbert spaces and then discuss the theory of linear operators on Hilbert spaces.
The needed results from Functional Analysis will be detailed in class. Topics include d then are the spectral theorem and its applications, compact operators, trace class and Hilbert Schmidt operators, unbounded self-adjoint operators.
Books: Reed&Simon , Functional Analysis I, Operator Theory part 4, by Simon.
Real Analysis, Complex Analysis, Linear Algebra