4 papers
Uniform bounds for Neumann heat kernels and their traces in convex sets
Rupert L. Frank, Simon Larson
We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends…
A Jensen inequality for partial traces and applications to partially semiclassical limits
Eric A. Carlen, Rupert L. Frank, Simon Larson
We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application we reprove and extend some theorems about eigenvalue asymptotics of…
Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian
Rupert L. Frank, Simon Larson, Paul Pfeiffer
The Berezin--Li--Yau and the Kröger inequalities show that Riesz means of order of the eigenvalues of the Laplacian on a domain of finite measure are bounded in terms…
Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Rupert L. Frank, Bernard Helffer, Ari Laptev
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results i…