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On Instability of the absolutely continuous spectrum of dissipative Schrödinger operators and Jacobi matrices


Author: R. Romanov
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 2.
Journal: St. Petersburg Math. J. 17 (2006), 325-341
MSC (2000): Primary 34L10, 47B44
Published electronically: February 20, 2006
MathSciNet review: 2159588
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Abstract: The absence of the absolutely continuous spectrum is proved for dissipative Schrödinger operators and Jacobi matrices with slowly decaying imaginary part of the potential.


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Additional Information

R. Romanov
Affiliation: School of Computer Science, Cardiff University, Cardiff, Queen’s Buildings, PO Box 916, Newport Road, Cardiff CF24 3XF, United Kingdom, and Laboratory of Quantum Networks, Institute for Physics, St. Petersburg State University, St. Petersburg 198504, Russia
Email: roma@rvr.stud.pu.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00907-1
Keywords: Absolutely continuous subspace, dissipative operators, Schr\"odinger operator
Received by editor(s): January 14, 2004
Published electronically: February 20, 2006
Additional Notes: The author was supported in part by EPSRC Grant GR/R20885 and by RFBR (grant no. 00-01-00479).
Article copyright: © Copyright 2006 American Mathematical Society