Frank, Rupert L. (2017) Eigenvalue bounds for the fractional Laplacian: A review. In: Recent Developments in Nonlocal Theory. De Gruyter , Berlin, pp. 210-235. ISBN 9783110571561. https://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290
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Abstract
We review some recent results on eigenvalues of fractional Laplacians and fractional Schrödinger operators.We discuss, in particular, Lieb–Thirring inequalities and their generalizations, as well as semi-classical asymptotics.
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| Additional Information: | © 2018 Rupert L. Frank, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License. The author would like to thank B. Dyda, L.Geisinger, E. Lenzmann, E. Lieb, R. Seiringer and L. Silvestre for collaborations involving the fractional Laplacian. He thanks R. Bañuelos, M. Kwaśnicki, F. Maggi and R. Song for helpful comments. Partial support by U.S. National Science Foundation DMS-1363432 is acknowledged. | |||||||||
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| DOI: | 10.1515/9783110571561-007 | |||||||||
| Record Number: | CaltechAUTHORS:20170501-092157290 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290 | |||||||||
| Official Citation: | Rupert L. Frank (2017). Eigenvalue Bounds for the Fractional Laplacian: A Review. In Giampiero Palatucci, Tuomo Kuusi (Eds.), Recent Developments in Nonlocal Theory (pp. 210–235). Warsaw, Poland: De Gruyter Open. https://doi.org/10.1515/9783110571561-007 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 77096 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 01 May 2017 16:27 | |||||||||
| Last Modified: | 15 Nov 2021 17:28 |
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