%0 Journal Article
%T Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem
%A Christian Remling
%J Mathematics
%D 2010
%I arXiv
%X If a Jacobi matrix $J$ is reflectionless on $(-2,2)$ and has a single $a_{n_0}$ equal to 1, then $J$ is the free Jacobi matrix $a_n\equiv 1$, $b_n\equiv 0$. I'll discuss this result and its generalization to arbitrary sets and present several applications, including the following: if a Jacobi matrix has some portion of its $a_n$'s close to 1, then one assumption in the Denisov-Rakhmanov Theorem can be dropped.
%U http://arxiv.org/abs/1006.2780v1