On m-accretive Schrödinger-type operators with singular potentials on Riemannian manifolds

Abstract

We consider a Schrödinger-type differential expression H V = ∇ ∗ ∇ + V , where ∇ is a Hermitian connection on a Hermitian vector bundle E over a complete Riemannian manifold ( M , g ) with metric g and positive smooth measure d μ , and V is a locally integrable section of the bundle of endomorphisms of E . We give a sufficient condition for m -accretivity of a realization of H V in L 2 ( E ) .