A course in measure theory at the level of UBC's
Math 420/Math 507.
It would be desirable to have also taken a
course on Hilbert and/or Banach spaces like UBC's
Math 421/Math 510, but this is not essential. I will adjust the
level of the course according to what proportion of the class
have taken such a course.
Text
Michael Reed and Barry Simon, Functional Analysis
(Methods of modern mathematical physics, volume 1, Academic Press, 1980).
This is an excellent book, but it is also unconscionably expensive.
So I have not made it a required textbook.
I will post all handouts, problem sets, etc. on the web
here.
Topics
Review of Hilbert and Banach Spaces: Definitions, examples, elementary geometry
Operators - linear, bounded, compact, hermitian, self-adjoint, unitary
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.
Unbounded Operators: Examples
Closed and preclosed unbounded operators
Self--adjoint extensions of hermitian operators
Bloch theory and the spectrum of periodic Schrödinger operators
Grading
The grade will be based on regular problem sets.
Policies
Missing a homework normally results in a mark of 0.
Exceptions may be granted in two cases: prior consent of the instructor
or a medical emergency.