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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

On selfadjoint extensions of some difference operator


Author: R. M. Kashaev
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 17 (2005), nomer 1.
Journal: St. Petersburg Math. J. 17 (2006), 157-167
MSC (2000): Primary 39A70, 47B25
Published electronically: January 19, 2006
MathSciNet review: 2140680
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Abstract | References | Similar Articles | Additional Information

Abstract: A one-parameter family of selfadjoint extensions is presented for the operator

$\displaystyle 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

$\displaystyle [p,q]=pq-qp=(2\pi i)^{-1}.$

The corresponding spectral problem is also solved.


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Additional 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

DOI: https://doi.org/10.1090/S1061-0022-06-00898-3
Keywords: Heisenberg commutation relation, discrete Liouville equation, selfadjoint extensions
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).
Dedicated: Dedicated to L. D. Faddeev on the occasion of his 70th birthday
Article copyright: © Copyright 2006 American Mathematical Society