Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem

الأصل · EN

If a Jacobi matrix J is reflectionless on (-2,2) and has a single aₙ₀ equal to 1, then J is the free Jacobi matrix aₙ≡ 1, bₙ≡ 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 aₙ's close to 1, then one assumption in the Denisov-Rakhmanov Theorem can be dropped.