Sharper estimates on the eigenvalues of Dirichlet fractional Laplacian
Selma Yildirim Yolcu Türkay Yolcu
Discrete & Continuous Dynamical Systems - A 2015, 35(5): 2209-2225 doi: 10.3934/dcds.2015.35.2209
This article is to analyze certain bounds for the sums of eigenvalues of the Dirichlet fractional Laplacian operator $(-\Delta)^{\alpha/2}|_{\Omega}$ restricted to a bounded domain $\Omega\subset{\mathbb R}^d$ with $d=2,$ $1\leq \alpha\leq 2$ and $d\geq 3,$ $0< \alpha\le 2$. A primary topic is the refinement of the Berezin-Li-Yau inequality for the fractional Laplacian eigenvalues. Our result advances the estimates recently established by Wei, Sun and Zheng in [34]. Another aspect of interest in this work is that we obtain some estimates for the sums of powers of the eigenvalues of the fractional Laplacian operator.
keywords: Klein-Gordon stable process Berezin-Li-Yau Eigenvalue non-local operator. inequality estimate fractional Laplacian

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