On m‐accretive Schrödinger‐type operators with singular potentials on manifolds of bounded geometry

Abstract

We consider a Schrödinger‐type differential expression ∇∗ ∇+V, where ∇ is a C∞‐bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry (M, g) with positive C∞‐bounded measure dμ, and V is a locally integrable linear bundle endomorphism. We define a realization of ∇∗ ∇+V in L2(E) and give a sufficient condition for its m‐accretiveness. The proof essentially follows the scheme of T. Kato, but it requires the use of a more general version of Kato′s inequality for Bochner Laplacian operator as well as a result on the positivity of solution to a certain differential equation on M.