Operateur de Schrodinger avec potentiel singulier multi-polaire (Schrodinger operator with a potential including several inverse-square singularities)

Abstract

Let P be the operator $-Δ+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical measures. This inequality implies local smoothing effect on the corresponding Schrodinger equation.