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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.

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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 Paper
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.
Funding AgencyGrant Number
Knut and Alice Wallenberg FoundationKAW 2018.0281
Issue or Number:4
Record Number:CaltechAUTHORS:20200420-145908047
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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
Deposited By: Tony Diaz
Deposited On:20 Apr 2020 23:20
Last Modified:16 Nov 2021 18:14

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