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Eigenvalue bounds for Schrödinger operators with complex potentials

Frank, Rupert L. (2011) Eigenvalue bounds for Schrödinger operators with complex potentials. Bulletin of the London Mathematical Society, 43 (4). pp. 745-750. ISSN 0024-6093. https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391

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Abstract

We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz and Sogge.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1112/blms/bdr008DOIArticle
http://onlinelibrary.wiley.com/doi/10.1112/blms/bdr008/abstractPublisherArticle
https://arxiv.org/abs/1005.2785arXivDiscussion Paper
Additional Information:© 2011 London Mathematical Society. Received 17 May 2010; revised 20 January 2011; published online 6 April 2011. The author wishes to thank A. Laptev and O. Safronov for useful correspondence.
Issue or Number:4
Classification Code:2000 Mathematics Subject Classification: 35P15 (primary), 35J10, 47F05 (secondary)
Record Number:CaltechAUTHORS:20170501-065723391
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391
Official Citation:Frank, R. L. (2011), Eigenvalue bounds for Schrödinger operators with complex potentials. Bulletin of the London Mathematical Society, 43: 745–750. doi:10.1112/blms/bdr008
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77079
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 16:57
Last Modified:03 Oct 2019 17:53

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