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ISSN 1088-6826(e) ISSN 0002-9939(p)

On a sum rule for Schrödinger operators with complex potentials

Author(s): Oleg Safronov
Journal: Proc. Amer. Math. Soc. 138 (2010), 2107-2112.
MSC (2000): Primary 47F05
Posted: January 22, 2010
MathSciNet review: 2596049
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Abstract: We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential . We prove that if $\vert V\vert$ decays faster than the Coulomb potential, then the series of imaginary parts of square roots of eigenvalues is convergent.

References:

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3.: Demuth, M., Hansmann, M. and Katriel G.: On the distribution of eigenvalues of non-selfadjoint operators, preprint.
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Additional Information:

Oleg Safronov
Affiliation: Department of Mathematics, University of North Carolina, Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223-0001
Email: osafrono@uncc.edu

DOI: 10.1090/S0002-9939-10-10248-2
PII: S 0002-9939(10)10248-2
Keywords: Eigenvalue estimates, Schr\"odinger operators, complex potentials, sum rules
Received by editor(s): April 10, 2009,
Received by editor(s) in revised form: October 4, 2009
Posted: January 22, 2010
Additional Notes: The author would like to thank B. Vainberg, S. Molchanov, A. Gordon and P. Grigoriev for inspiring and motivating discussions
Communicated by: Varghese Mathai
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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