Self‐adjointness of non‐semibounded covariant Schrödinger operators on Riemannian manifolds

Abstract In the context of a geodesically complete Riemannian manifold M , we study self‐adjointness where ∇ is metric covariant derivative (with formal adjoint ) on Hermitian vector bundle over and V locally square integrable section such that (fiberwise) norm “negative” part belongs to local Kato class (or, more generally, contractive Dynkin class). Instead lower semiboundedness hypothesis, assume there exists number positive function q satisfying certain growth conditions, inequality being understood in quadratic form sense . first result, which pertains case use elliptic equation method. second hyperbolic