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.
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| 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. | |||||||||
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| 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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