15 citations · 46 across the 7 of their papers we have counts for
6 papers · 1 filter
A short proof of Weyl's law for fractional differential operators
Leander Geisinger
We study spectral asymptotics for a large class of differential operators on an open subset of with finite volume. This class includes the Dirichlet Laplacian, the fractiona…
Semi-classical analysis of the Laplace operator with Robin boundary conditions
Rupert L. Frank, Leander Geisinger
We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove…
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…
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…
Sharp spectral estimates in domains of infinite volume
Leander Geisinger, Timo Weidl
We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - an…
Geometrical Versions of improved Berezin-Li-Yau Inequalities
Leander Geisinger, Ari Laptev, Timo Weidl
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in , . In particular, we derive upper bounds on Riesz means of order $σ…