Rate of decay at high energy of local spectral projections associated with Schrödinger operators (Q1262465)

Let \(H=-(1/2)\Delta +V(x)\) be a Schrödinger operator defined on \(S({\mathbb{R}}^ n)\) with a potential V satisfying \(| \partial^{\alpha}_ xV(x)| \leq C_{\alpha}(1+| x|^ 2)^{(m-| \alpha |)/2}.\) Let \(\bar H\) be a selfadjoint extension of H on \(L^ 2({\mathbb{R}}^ n)\). The author studies the rate of decay of high energy of the local spectral projections of \(\bar H.\)