We prove controllability of the Schrödinger equation in ℝ d in any time T> 0 with internal
control supported on nonempty, periodic, open sets. This demonstrates in particular that …

We prove and apply two theorems: first, a quantitative, scale-free unique continuation
estimate for functions in a spectral subspace of a Schrödinger operator on a bounded or …

We survey recent results on the control problem for the heat equation on unbounded and
large bounded domains. First we formulate new uncertainty relations, respectively spectral …

We prove that localization near band edges of multi-dimensional ergodic random
Schrödinger operators with periodic background potential in L^ 2 (R^ d) L 2 (R d) is …

We prove a spectral inequality for the Landau operator. This means that for all $ f $ in the
spectral subspace corresponding to energies up to $ E $, the $ L^ 2$-integral over suitable …

Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of
Schrödinger operators are extended to allow singular potentials such as certain L p …

We consider elliptic second order partial differential operators with Lipschitz continuous
leading order coefficients on finite cubes and the whole Euclidean space. We prove …

We prove and apply two theorems: First, a quantitative, scale-free unique continuation
estimate for functions in a spectral subspace of a Schr\" odinger operator on a bounded or …