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Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples |
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| Authors: | Anne Boutet de Monvel Jan Janas Serguei Naboko |
| Affiliation: | 1. Institut de Math??matiques de Jussieu, Universit?? Paris Diderot Paris 7, 175 rue du Chevaleret, 75013, Paris, France 2. Institute of Mathematics, Polish Academy of Sciences, ul. ?w. Tomasza 30, 31-027, Krak??w, Poland 3. Department of Mathematical Physics, Institute of Physics, St. Petersburg University, Ulianovskaia 1, 198904, St. Petergoff, St. Petersburg, Russia |
| 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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