81 citations · 167 across the 10 of their papers we have counts for
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Estimates for the Lowest Eigenvalue of Magnetic Laplacians
Tomas Ekholm, Hynek Kovarik, Fabian Portmann
We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower an…
A Magnetic Contribution to the Hardy Inequality
Tomas Ekholm, Fabian Portmann
We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic f…
Lieb-Thirring Inequalities for Fourth-Order Operators in Low Dimensions
Tomas Ekholm, Andreas Enblom
This paper considers Lieb-Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace in…
Schroedinger Operators on Regular Metric Trees with Long Range Potentials: Weak Coupling Behavior
Tomas Ekholm, Andreas Enblom, Hynek Kovarik
Consider a regular -dimensional metric tree with root . Define the Schroedinger operator , where is a non-negative, symmetric potential, on , with Neumann b…
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…
Lieb-Thirring inequalities on the half-line with critical exponent
Tomas Ekholm, Rupert L. Frank
We consider a Schrödinger operator on the half-line with a Dirichlet boundary condition at the origin and show that moments of its negative eigenvalues can be estimated by the part…