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Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group

Frank, Rupert L. and Laptev, Ari (2010) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. International Mathematics Research Notices, 2010 (15). pp. 2889-2902. ISSN 1073-7928. https://resolver.caltech.edu/CaltechAUTHORS:20170526-092032067

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Abstract

We prove that for any domain in the Heisenberg group the (k+1)'th Neumann eigenvalue of the sub-Laplacian is strictly less than the k'th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/imrn/rnp230DOIArticle
https://academic.oup.com/imrn/article/2010/15/2889/766954/Inequalities-between-Dirichlet-and-NeumannPublisherArticle
https://arxiv.org/abs/0906.1402arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© The Author 2010. Published by Oxford University Press. Received June 8, 2009; Accepted December 2, 2009 Communicated by Prof. Peter Sarnak The authors acknowledge interesting discussions with A. Hansson concerning the topics of this paper. The first author wishes to thank E. Lieb and R. Seiringer for helpful remarks. Support through DFG grant FR 2664/1-1 and U.S. NSF grant PHY 06 52854 (R.F.) is gratefully acknowledged. Recently, Bernard Helffer suggested a way of proving similar estimates for a large class of sub-elliptic operators. This will be the subject of a forthcoming publication.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)FR 2664/1-1
NSFPHY-0652854
Issue or Number:15
Record Number:CaltechAUTHORS:20170526-092032067
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170526-092032067
Official Citation:Rupert L. Frank, Ari Laptev; Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group. Int Math Res Notices 2010; 2010 (15): 2889-2902. doi: 10.1093/imrn/rnp230
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77801
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 May 2017 18:58
Last Modified:09 Mar 2020 13:18

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