A separation property for magnetic Schr?dinger operators on Riemannian manifolds

摘要

We consider a Schr?dinger differential expression L=Δ_A+q on a complete Riemannian manifold (M,g) with metric g, where Δ_A is the magnetic Laplacian on M and q≥0 is a locally square integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L~2(M) if for all u∈L~2(M) such that Lu∈L~2(M), we have qu∈L~2(M). We give sufficient conditions for L to be separated in L~2(M).