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Eigenvalue bounds for Schrödinger operators with complex potentials. II

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.

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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
Related URLs:
URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Simon, Barry0000-0003-2561-8539
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).
Funding AgencyGrant Number
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
Record Number:CaltechAUTHORS:20170502-082840587
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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
Deposited By: Tony Diaz
Deposited On:02 May 2017 17:58
Last Modified:15 Nov 2021 17:28

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