Mathematics – Spectral Theory
Scientific paper
2010-06-14
Mathematics
Spectral Theory
Scientific paper
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.
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