# zbMATH — the first resource for mathematics

Semi-classical resolvent estimates for the Schrödinger operator on non-compact complete Riemannian manifolds. (English) Zbl 1159.58308
Summary: We prove uniform semi-classical estimates for the resolvent of the Schrödinger operator $$h^2\Delta_g + V(x)$$, $$0 < h \ll 1$$, at a nontrapping energy level $$E > 0$$, where $$V$$ is a real-valued non-negative potential and $$\Delta_g$$ denotes the positive Laplace-Beltrami operator on a non-compact complete Riemannian manifold which may have a nonempty compact smooth boundary.

##### MSC:
 58J05 Elliptic equations on manifolds, general theory 35J10 Schrödinger operator, Schrödinger equation 31C12 Potential theory on Riemannian manifolds and other spaces 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
Full Text: