Semi‐classical resolvent estimates and regions free of resonances

We prove resolvent estimates for self‐adjoint operators of the form P ( h ) = − h 2 Δ + V ( x , h )onL 2 ( R n ) , n ≥ 3 , where 0 < h ≪ 1 is a semi‐classical parameter and V = O ( h ν ) , ν > 0 , is a real‐valued potential. The potential is supposed to have very little regularity with respect to the radial variable, only. As a consequence, we obtain a region free of resonances in the case when V is of compact support.