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Transactions of the American Mathematical Society

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Eigenvalue bounds for Stark operators with complex potentials


Authors: Evgeny Korotyaev and Oleg Safronov
Journal: Trans. Amer. Math. Soc. 373 (2020), 971-1008
MSC (2010): Primary 35P15; Secondary 47A75
DOI: https://doi.org/10.1090/tran/7873
Published electronically: November 5, 2019
MathSciNet review: 4068256
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Abstract | Similar Articles | Additional Information

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

Keywords: Stark operators, complex potentials, eigenvalue estimates
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.
Article copyright: © Copyright 2019 American Mathematical Society