4 papers
Szegö limit theorem and Heisenberg Laplacian
Jiyu Fan, Ari Laptev
The aim of this paper is to obtain a version of the classical Szegö limit theorem, where instead of the operator of second derivative on a circle we consider the Heisenberg-Hörmand…
Time dependent Schrödinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field
Jiyu Fan, Ari Laptev
We construct an approximation of the kernel of the solution of the time dependent Schrödinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic field…
Eigenvalue lower bounds through a generalized inradius
Rupert L. Frank, Ari Laptev, Durvudkhan Suragan
Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for ei…
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…