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Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem
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Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem
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Journal Article
Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem
2011
Overview
If a Jacobi matrix JJ is reflectionless on (−2,2)(-2,2) and has a single an0a_{n_0} equal to 11, then JJ is the free Jacobi matrix an≡1a_n\\equiv 1, bn≡0b_n\\equiv 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 ana_n’s close to 11, then one assumption in the Denisov-Rakhmanov Theorem can be dropped.
Publisher
American Mathematical Society
