Netanel Levi: Alpha-Subordinacy Theory of Schroedinger Operators on Z

Speaker
Netanel Levi, Hebrew University of Jerusalem

Abstract
In the context of Schroedinger operators on graphs, subordinacy theory relates asymptotic properties of solutions to the eigenvalue equation to continuity properties of the spectral measures. This theory was originally developed in the half-line case by Gilbert and Pearson (1987), and was later generalized and refined in many ways. Jitomirskaya and Last (1999) developed \(\alpha\)-subordinacy theory, which treats more subtle continuity properties of the spectral measures, and it was conjectured by Damanik, Killip and Lenz (DKL) that this type of connection should also hold in the line case. In this talk, we present some new results towards the resolution of the DKL conjecture. If time allows, we will also discuss an example of a Schroedinger operator on \(Z\) with some interesting properties. Based on joint work with Yoram Last.