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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical range


Author: Marcel Hansmann
Journal: Proc. Amer. Math. Soc. 142 (2014), 1321-1335
MSC (2010): Primary 47A75, 47A12, 35J10, 47B36
Published electronically: January 29, 2014
MathSciNet review: 3162253
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Abstract: We use a classical result of Hildebrandt to establish simple conditions for the absence of eigenvalues of non-selfadjoint discrete and continuous Schrödinger operators on the boundary of their numerical range.


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Additional Information

Marcel Hansmann
Affiliation: Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
Email: marcel.hansmann@mathematik.tu-chemnitz.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11885-5
Keywords: Schr\"odinger operators, non-selfadjoint, complex potentials, eigenvalues, numerical range
Received by editor(s): August 5, 2011
Received by editor(s) in revised form: May 16, 2012
Published electronically: January 29, 2014
Communicated by: Michael Hitrik
Article copyright: © Copyright 2014 American Mathematical Society