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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Eigenvalue bounds for Stark operators with complex potentials
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by Evgeny Korotyaev and Oleg Safronov PDF
Trans. Amer. Math. Soc. 373 (2020), 971-1008 Request permission

Abstract:

We consider the three-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper half-plane.
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Additional Information
  • Evgeny Korotyaev
  • Affiliation: Saint-Petersburg State University, Universitetskaya naberezhnaya 7/9, St. Petersburg 199034, Russia
  • MR Author ID: 211673
  • Email: korotyaev@gmail.com; e.korotyaev@spbu.ru
  • Oleg Safronov
  • Affiliation: Department of Mathematics and Statistics, UNCC, Charlotte, North Carolina
  • MR Author ID: 607478
  • Email: osafrono@uncc.edu
  • Received by editor(s): February 12, 2018
  • Received by editor(s) in revised form: February 19, 2018, January 6, 2019, February 8, 2019, and April 9, 2019
  • Published electronically: November 5, 2019
  • Additional Notes: The first author was supported by RSF Grant No. 18-11-00032.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 971-1008
  • MSC (2010): Primary 35P15; Secondary 47A75
  • DOI: https://doi.org/10.1090/tran/7873
  • MathSciNet review: 4068256