11/10/2004

Barry Simon
Caltech

The Sharp Form of the Strong Szego Theorem

This talk will discuss a proof of the Strong Szego theorem on the second term in the asymptotics of Toeplitz determinants.  After a brief discussion of the history, I'll discuss the elementary argument that reduces the sharp (optimal) result to the case of analytic symbols.  I'll then present a new proof of the theorem in the analytic case.  I'll present the necessary background from the theory of orthogonal polynomials on the unit circle along the way.