Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II. Journal of Spectral Theory, 7 (3). pp. 633-658. ISSN 1664-039X. doi:10.4171/JST/173. https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587
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Abstract
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator -Δ+V in L^2 (R^ν) with complex potential has absolute value at most a constant times ||V||^(γ+ν/2)/γ)_(γ+ν/2) for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2017 European Mathematical Society. Received April 5, 2015; revised May 26, 2015. Published online: 2017-09-28. Work partially supported by U.S. National Science Foundation grants PHY-1347399, DMS-1363432 (R. L. Frank), and DMS-1265592 (B. Simon). | ||||||||||||
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Subject Keywords: | Schrödinger operator, complex-valued potential, eigenvalue bounds, embedded eigenvalue | ||||||||||||
Issue or Number: | 3 | ||||||||||||
Classification Code: | Mathematics Subject Classification (2010): Primary 35P15; Secondary 81Q12 | ||||||||||||
DOI: | 10.4171/JST/173 | ||||||||||||
Record Number: | CaltechAUTHORS:20170502-082840587 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 | ||||||||||||
Official Citation: | Frank Rupert, Simon Barry: Eigenvalue bounds for Schrödinger operators with complex potentials. II. J. Spectr. Theory 7 (2017), 633-658. doi: 10.4171/JST/173 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 77120 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 02 May 2017 17:58 | ||||||||||||
Last Modified: | 15 Nov 2021 17:28 |
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