Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem

Author:
Christian Remling

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2175-2182

MSC (2010):
Primary 42C05, 47B36, 81Q10

DOI:
https://doi.org/10.1090/S0002-9939-2010-10747-5

Published electronically:
November 30, 2010

MathSciNet review:
2775395

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Abstract: If a Jacobi matrix is reflectionless on and has a single equal to , then is the free Jacobi matrix , . 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 's close to , then one assumption in the Denisov-Rakhmanov Theorem can be dropped.

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Additional Information

**Christian Remling**

Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Email:
cremling@math.ou.edu

DOI:
https://doi.org/10.1090/S0002-9939-2010-10747-5

Keywords:
Reflectionless Jacobi matrix,
Denisov-Rakhmanov Theorem

Received by editor(s):
June 14, 2010

Published electronically:
November 30, 2010

Additional Notes:
The author’s work was supported by NSF grant DMS 0758594

Communicated by:
Walter Van Assche

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.