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Published 2017 | Version Published + Submitted
Book Section - Chapter Open

Eigenvalue bounds for the fractional Laplacian: A review

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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.

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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Published - _9783110571561_-_Recent_Developments_in_Nonlocal_Theory__Eigenvalue_Bounds_for_the_Fractional_Laplacian_A_Review.pdf

Submitted - 1603.09736.pdf

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1603.09736.pdf

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Eprint ID
77096
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CaltechAUTHORS:20170501-092157290

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https://arxiv.org/abs/1603.09736 (URL)

Funding

NSF
DMS-1363432

Dates

Created
2017-05-01
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Updated
2021-11-15
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