Mathematics 511, Section 101

Operator Theory and Applications

Department of Mathematics University of British Columbia


Instructor

Joel Feldman

 E-mail    feldman@math.ubc.ca 
 Office  Math 221
 Phone  604-822-5660
 Home page  http://www.math.ubc.ca/~feldman/
 Office hours   Mon 2:30-3:30, Tue 2:00-3:00, Thr 10:00-11:00

Prerequisites


Text

I will post all handouts, problem sets, etc. on the web here.


Topics

  1. Review of Hilbert and Banach Spaces:
     Definitions, examples, elementary geometry
     Operators - linear, bounded, compact, hermitian, self-adjoint, unitary
  2. The Spectral Theorems:
     I will state several versions of the spectral theorem. The extent to which this is treated as a review, and in particular how many proofs I give, will depend on what proportion of the class has already seen rigorous proofs of one or more variants of the spectral theorem.
  3. Unbounded Operators:
     Examples
     Closed and preclosed unbounded operators
     Self--adjoint extensions of hermitian operators
     Bloch theory and the spectrum of periodic Schrödinger operators

Grading


Policies