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The Marchenko representation of reflectionless Jacobi and Schrödinger operators


Authors: Injo Hur, Matt McBride and Christian Remling
Journal: Trans. Amer. Math. Soc. 368 (2016), 1251-1270
MSC (2010): Primary 34L40, 47B36, 81Q10
DOI: https://doi.org/10.1090/S0002-9947-2015-06527-1
Published electronically: February 3, 2015
MathSciNet review: 3430363
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Abstract: We consider Jacobi matrices and Schrödinger operators that are reflectionless on an interval. We give a systematic development of a certain parametrization of this class, in terms of suitable spectral data, that is due to Marchenko. Then some applications of these ideas are discussed.


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Additional Information

Injo Hur
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: ihur@math.ou.edu

Matt McBride
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: mmcbride@math.ou.edu

Christian Remling
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: cremling@math.ou.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06527-1
Keywords: Jacobi matrix, Schr\"odinger operator, reflectionless
Received by editor(s): January 29, 2014
Published electronically: February 3, 2015
Additional Notes: The third author’s work was supported by NSF grant DMS 1200553
Article copyright: © Copyright 2015 American Mathematical Society