On selfadjoint extensions of some difference operator
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R. M. Kashaev
Translated by: A. Plotkin - St. Petersburg Math. J. 17 (2006), 157-167
- DOI: https://doi.org/10.1090/S1061-0022-06-00898-3
- Published electronically: January 19, 2006
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Abstract:
A one-parameter family of selfadjoint extensions is presented for the operator \[ L=-e^{2\pi p}+2\cosh (z\pi bq), \] where $0<b\le 1$ and $p$ and $q$ are unbounded selfadjoint operators satisfying the Heisenberg commutation relation \[ [p,q]=pq-qp=(2\pi i)^{-1}.\] The corresponding spectral problem is also solved.References
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Bibliographic Information
- R. M. Kashaev
- Affiliation: Université de Genève, Section de mathématiques, 2-4, rue du Lièvre, CP 240, 1211 Genève 24, Suisse
- Email: Rinat.Kashaev@math.unige.ch
- Received by editor(s): September 15, 2004
- Published electronically: January 19, 2006
- Additional Notes: The author was supported in part by the Swiss National Science Foundation and by RFBR (grant no. 02-01-00085).
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 157-167
- MSC (2000): Primary 39A70, 47B25
- DOI: https://doi.org/10.1090/S1061-0022-06-00898-3
- MathSciNet review: 2140680
Dedicated: Dedicated to L. D. Faddeev on the occasion of his 70th birthday