Mathematical Physics Seminar
Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations
Barry Simon,
Mathematics Department,
California Institute of Technology,
After defining 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 Gambo, Nagel and Rouault who obtain the sum rules using large deviations for random matrices.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].
Event Series
Mathematical Physics Seminar Series
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