Eigenvalue bounds for the fractional Laplacian: A review
Rupert L. Frank
TL;DR
This paper reviews recent advances in understanding eigenvalues of fractional Laplacians and Schrödinger operators, focusing on inequalities and asymptotic behaviors relevant to mathematical physics.
Contribution
It synthesizes recent results on eigenvalue bounds, Lieb-Thirring inequalities, and semi-classical asymptotics for fractional operators.
Findings
Overview of Lieb-Thirring inequalities for fractional Laplacians
Discussion of semi-classical asymptotics for fractional operators
Summary of generalizations and recent developments in the field
Abstract
We review some recent results on eigenvalues of fractional Laplacians and fractional Schr\"odinger operators. We discuss, in particular, Lieb-Thirring inequalities and their generalizations, as well as semi-classical asymptotics.
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