| Barry Simon
California Institute of Technology
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Lunedì 28 Maggio 2018, ore 16:30
Aula Chisini, Diparimento di Matematica, Via C. Saldini 50 |
|
|
Abstract
|
 |
 |
After de ning the spectral theory of orthogonal polynomials on the unit circle
(OPUC) and real line (OPRL), I'll describe Verblunsky's version of Szego's
theorem as a sum rule for OPUC and the Killip-Simon sum rule for OPRL
and their spectral consequences. Next I'll explain the original proof of Killip-Simon using representation theorems for meromorphic Herglotz functions.
Finally I'll focus on recent work of Gamboa, Nagel and Rouault who obtain
the sum rules using large deviations for random matrices. |
|
|
|
|
|
