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)


Preliminary Syllabus:

  1. Introduction and Overview
  2. Szego's Theorem for OPUC
  3. Three Kinds of Polynomial Asymptotics, I
  4. Three Kinds of Polynomial Asympotics, II
  5. Killip-Simon Theorem on [-2,2]
  6. Szego Asymptotics and Shohat-Nevai for [-2; 2]
  7. Periodic OPRL
  8. Finite Gap Isospectral Torus


Recommended Literature:

  1. [OPUC] B. Simon, Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Series 54.1, AMS, Providence, RI, 2005.
  2. [OPUC2] B. Simon, Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium Series, 54.2, AMS, Providence, RI, 2005.
  3. [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.