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