Sharper estimates on the eigenvalues of Dirichlet fractional Laplacian
Sharper estimates on the eigenvalues of Dirichlet fractional Laplacian
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 …