In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schr\"odinger operator in $ \mathbb{ R}^d$ \begin{ equation*} H_{ g,V} = \Delta_g + V(x), \end{ equation*} where $\Delta_g$ is the Laplace-Beltrami operator with respect to an analytic metric $g$, which is a perturbation of the Euclidean metric, and $V(x)$ a real valued analytic potential vanishing at infinity.
Categories: math.AP