Abstract
We give explicit examples of unbounded Jacobi operators with a few gaps in their essential spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum fills any finite number of bounded intervals is considered. Their point spectrum accumulates to +∞ and −∞. The asymptotics of large eigenvalues is also found.
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Acknowledgements
J. J. is supported in part by “INTAS” and in part by MSHE grant N N201 426533. S. N. is supported in part by “INTAS” and in part by RFBR grant 09-01-00515a. S. N. is also grateful to the Université Paris Diderot (where a part of this work has been done) for its hospitality.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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de Monvel, A.B., Janas, J. & Naboko, S. Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples. Integr. Equ. Oper. Theory 69, 151–170 (2011). https://doi.org/10.1007/s00020-010-1856-x
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DOI: https://doi.org/10.1007/s00020-010-1856-x