391 citations · 1.8k across the 147 of their papers we have counts for
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Counting Negative Eigenvalues for the Magnetic Pauli Operator
Søren Fournais, Rupert L. Frank, Magnus Goffeng +2
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues remi…
Asymptotics of singular values for quantum derivatives
Rupert L. Frank, Fedor Sukochev, Dmitriy Zanin
We obtain Weyl type asymptotics for the quantised derivative $\dbar f$ of a function from the homgeneous Sobolev space on The asympt…
Weyl's law under minimal assumptions
Rupert L. Frank
We show that Weyl's law for the number and the Riesz means of negative eigenvalues of Schrödinger operators remains valid under minimal assumptions on the potential, the vector pot…
Discrete Schrödinger operators with decaying and oscillating potentials
Rupert L. Frank, Simon Larson
We study a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential $V(n)=λn^{-α}\cos(…
Semiclassical asymptotics for a class of singular Schrödinger operators
Rupert L. Frank, Simon Larson
Let be bounded with boundary. In this paper we consider Schrödinger operators on with as $\m…
On the error in the two-term Weyl formula for the Dirichlet Laplacian
Rupert L. Frank, Simon Larson
We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of . In particular, f…