Spectral Theory and the Sum Rules for Jacobi Matrices and Orthogonal Polynomials

Abstract: The sum rules (aka trace formulae) for Jacobi matrices, a powerful tool of spectral theory, are relations between the coefficients of the matrix on one hand and its spectral measure on the other. I will discuss some recent developments in the area and their applications to questions about the spectral types of Jacobi matrices and Schrodinger operators. Related problems for orthogonal polynomials on the unit circle will also be discussed.

Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).