Three theorems are given including sketches of their proofs. They deal with the resolvent of \((-\Delta -k^ 2)\) in a domain D in \({\mathbb{R}}^ n\), and in \(\pm Im k>0\). In each case with respect to k the first theorem concerns analytic continuation of the resolvent, the second is an estimate for Green’s function, and the third gives an inequality for the solution of a scattering problem.