391 citations · 1.8k across the 147 of their papers we have counts for
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Spectral inequalities for Schroedinger operators with surface potentials
Rupert L. Frank, Ari Laptev
We prove sharp Lieb-Thirring inequalities for Schroedinger operators with potentials supported on a hyperplane and we show how these estimates are related to Lieb-Thirring inequali…
Remarks about Hardy inequalities on metric trees
Tomas Ekholm, Rupert L. Frank, Hynek Kovarik
We find sharp conditions on the growth of a rooted regular metric tree such that the Neumann Laplacian on the tree satisfies a Hardy inequality. In particular, we consider homogene…
Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer
We give a CLR type bound on the number of bound states of Schroedinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly impr…
Eigenvalue estimates for the Aharonov-Bohm operator in a domain
Rupert L. Frank, Anders Hansson
We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generaliz…
Polya's conjecture in the presence of a constant magnetic field
Rupert L. Frank, Michael Loss, Timo Weidl
We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue esti…
Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
Rupert L. Frank, Barry Simon, Timo Weidl
We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Ja…