Math 961: Unbounded operators
Mon,
Wed, Fri 9:30 AM, Smith Lab 1180
Office
hours: Mon, Wed, Fri 10:30 AM, MW 404
Topics covered:
- Basics of bounded operators
- Unbounded operators
- Self-adjointness
- Spectral measures
- The spectral theorem
- Extensions of symmetric operators
- Quadratic forms
- Polar decomposition
- Propagators
- Applications to PDEs, the Laplacian, elliptic
regularity,
Schrödinger operators, analytic and asymptotic perturbation
theory
Bibliography:
Reed and B. Simon, Methods of
Modern Mathematical Physics, Academic Press, New York, 1972.
T Kato, Perturbation Theory for Linear Operators, Springer Verlag
(1995).
R. Douglas, Banach Algebra Techniques in Operator Theory, Vol. 179,
Springer-Verlag New York, (1998).
Class notes ( I update
these notes frequently, so please look for the latest version. This version is as of June 6, 2011 )