A Classical Approximation Point of View on Some Results in the Spectral Theory of Jacobi Matrices

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR
Topic:A Classical Approximation Point of View on Some Results in the Spectral Theory of Jacobi Matrices
Speaker:Mira Shamis
Affiliation:Member, School of Mathematics
Date:Friday, December 10
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/mathphys/2010/shamis

Deift--Simon and Poltoratskii--Remling proved upper bounds on the measure of the absolutely continuous spectrum of Jacobi matrices. Using methods of classical approximation theory, we give a new proof of their results, and generalize them in several ways. First, we prove a sharper inequality taking the distribution of the values of the potential into account. Second, we prove a generalization of a "local" inequality of Deift--Simon to the non-ergodic setting. Based on joint work with Sasha Sodin