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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a sum rule for Schrödinger operators with complex potentials
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by Oleg Safronov PDF
Proc. Amer. Math. Soc. 138 (2010), 2107-2112 Request permission

Abstract:

We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential $V$. We prove that if $|V|$ decays faster than the Coulomb potential, then the series of imaginary parts of square roots of eigenvalues is convergent.
References
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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
  • MR Author ID: 607478
  • Email: osafrono@uncc.edu
  • Received by editor(s): April 10, 2009
  • Received by editor(s) in revised form: October 4, 2009
  • Published electronically: 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 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 2107-2112
  • MSC (2000): Primary 47F05
  • DOI: https://doi.org/10.1090/S0002-9939-10-10248-2
  • MathSciNet review: 2596049