15 citations · 46 across the 7 of their papers we have counts for
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math.SP2011★ 12 cited
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain
Rupert L. Frank, Leander Geisinger
Let -Δdenote the Dirichlet Laplace operator on a bounded open set in \mathbb{R}^d. We study the sum of the negative eigenvalues of the operator -h^2 Δ- 1 in the semiclassical limit…
math.SP2011
Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator
Rupert L. Frank, Leander Geisinger
We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a t…