17 papers
Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators
Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu
We study random Schrödinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues rem…
Orthonormal Spectral Cluster Bounds on Manifolds with Nonpositive Curvature
Jean-Claude Cuenin, Ngoc Nhi Nguyen, Xiaoyan Su
Let be a closed -dimensional Riemannian manifold with nonpositive sectional curvature. We prove sharp, logarithmically improved spectral cluster bounds for orthonormal s…
Smoothing inequalities for transport metrics in compact spaces
Bence Borda, Jean-Claude Cuenin
We prove general upper estimates for the distance between two Borel probability measures in Wasserstein metric in terms of the Fourier transforms of the measures. We work in compac…
Spectral cluster bounds for orthonormal functions on manifolds with nonsmooth metrics
Jean-Claude Cuenin, Ngoc Nhi Nguyen, Xiaoyan Su
We establish spectral cluster bounds for families of orthonormal functions associated to the Laplace-Beltrami operator on a compact Riemannian manifold. The metric is only as…
Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
Jean-Claude Cuenin
We prove eigenvalue bounds for Schrödinger operator on compact manifolds with complex potentials . The bounds depend only on an -norm of the potential, and they ar…
Open problem: Violation of locality for Schrödinger operators with complex potentials
Jean-Claude Cuenin, Rupert L. Frank
We explain in which sense Schrödinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomen…