Probabilistic Averages of Jacobi Operators |
| |
Authors: | Helge Krüger |
| |
Affiliation: | 1. Department of Mathematics, Rice University, Houston, TX, 77005, USA
|
| |
Abstract: | I study the Lyapunov exponent and the integrated density of states for general Jacobi operators. The main result is that questions about these can be reduced to questions about ergodic Jacobi operators. I use this to show that for finite gap Jacobi operators, regularity implies that they are in the Cesàro–Nevai class, proving a conjecture of Barry Simon. Furthermore, I use this to study Jacobi operators with coefficients a(n) = 1 and b(n) = f(n ρ (mod 1)) for ρ > 0 not an integer. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|