摘要 : If a Jacobi matrix J is reflectionless on (-2, 2) and has a single a_(n0) equal to 1, then J is the free Jacobi matrix an ≡ 1, b_n ≡0. The paper discusses this result and its generalization to arbitrary sets and presents several a... 展开 If a Jacobi matrix J is reflectionless on (-2, 2) and has a single a_(n0) equal to 1, then J is the free Jacobi matrix an ≡ 1, b_n ≡0. The paper discusses this result and its generalization to arbitrary sets and presents 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. 收起