Spectral Theory of Orthogonal Polynomials
An informal postgraduate level lecture course at King's College London,
spring 2014.
Lecturer:
Professor Barry Simon
(California Institute of Technology)
Schedule:
- Tuesday 25 February, 10:00-12:00, room K3.11
- Wednesday 26 February, 13:00-15:00, room S-1.06 (level minus one)
- Tuesday 4 March, 10:00-12:00, room K3.11
- Wednesday 5 March, 13:00-15:00, room S-1.06 (level minus one)
Preliminary Syllabus:
- Introduction and Overview
- Szego's Theorem for OPUC
- Three Kinds of Polynomial Asymptotics, I
- Three Kinds of Polynomial Asympotics, II
- Killip-Simon Theorem on [-2,2]
- Szego Asymptotics and Shohat-Nevai for [-2; 2]
- Periodic OPRL
- Finite Gap Isospectral Torus
Slides:
Recommended Literature:
- [OPUC] B. Simon, Orthogonal Polynomials on the Unit Circle,
Part 1: Classical Theory,
AMS Colloquium Series 54.1,
AMS, Providence, RI, 2005.
- [OPUC2] B. Simon,
Orthogonal Polynomials on the Unit Circle,
Part 2: Spectral Theory,
AMS Colloquium Series, 54.2,
AMS, Providence, RI, 2005.
- [SzThm] B. Simon,
Szego's Theorem and Its Descendants:
Spectral Theory for L^2 Perturbations of Orthogonal Polynomials,
M. B. Porter Lectures, Princeton University Press, Princeton, NJ, 2011
Contact:
Alexander Pushnitski
alexander.pushnitski@kcl.ac.uk
Prof. Simon will be visiting London between 12 February and 6 March 2014.
During his stay, he will also give a colloquium talk on history of mathematics
on 13 February, 15:00-16:00, room S-3.20.
Prof. Simon's visit is supported by the
School of Natural and Mathematical
Sciences under the Distinguished Visitors programme.