Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein) (Q1076257)

The authors prove a strong unique continuation property: Let \(\Omega\) be a connected domain of \({\mathbb{R}}^ n\), \(x\in \Omega\), \(V\in L^{n/2}_{loc}({\mathbb{R}}^ n)\), \(q=2n/(n+2)\), \(u\in H^{2,q}_{loc}(\Omega)\), and \(u=0\) on some nonempty subset of \(\Omega\), then \(u=0\) on \(\Omega\). The method used is to prove a Carleman type inequality by complex interpolation. - The paper has an appendix by E. Stein where the proof is simplified and the result is extended to Lorentz spaces.