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On the error in the two-term Weyl formula for the Dirichlet Laplacian

Frank, Rupert L. and Larson, Simon (2020) On the error in the two-term Weyl formula for the Dirichlet Laplacian. Journal of Mathematical Physics, 61 (4). Art. No. 043504. ISSN 0022-2488. doi:10.1063/1.5145003. https://resolver.caltech.edu/CaltechAUTHORS:20200420-145908047

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Abstract

We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of R^d. In particular, for the short-time asymptotics of the trace of the heat kernel, we prove that the error term cannot be made quantitatively better than little-o of the second term.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.5145003DOIArticle
https://arxiv.org/abs/2001.01876arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Larson, Simon0000-0002-0057-8211
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 13 January 2020; Accepted: 24 March 2020; Published Online: 20 April 2020. We would like to dedicate this paper to the memory of Jean Bourgain. The U.S. National Science Foundation (Grant No. DMS-1363432) (R.L.F.) and Knut and Alice Wallenberg Foundation (Grant No. KAW 2018.0281) (S.L.) are acknowledged. The authors also wish to thank Institut Mittag-Leffler, where part of this work was carried out. Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Knut and Alice Wallenberg FoundationKAW 2018.0281
Issue or Number:4
DOI:10.1063/1.5145003
Record Number:CaltechAUTHORS:20200420-145908047
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200420-145908047
Official Citation:On the error in the two-term Weyl formula for the Dirichlet Laplacian. Rupert L. Frank and Simon Larson. Journal of Mathematical Physics 61:4; doi: 10.1063/1.5145003
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102669
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Apr 2020 23:20
Last Modified:16 Nov 2021 18:14

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