The m-accretivity of covariant Schrödinger operators with unbounded drift
We work in the context of a geodesically complete Riemannian n-manifold M with a Hermitian vector bundle V over M, equipped with a metric covariant derivative ∇. We study the operator H: = ∇ †∇ + ∇ X+ V, where ∇ † is the formal adjoint of ∇ , the symbol ∇ X stands for the action of ∇ along a smooth vector field X on M, and V is a locally bounded section of the endomorphism bundle End V. We show that under certain conditions on X and V, the closure H|Cc∞(V)¯ of H|Cc∞(V) in Lp(V) , where 1 < p< ∞, is a maximal accretive operator. We also show that H|Cc∞(V)¯ coincides with the “maximal” realization of H in Lp(V).
Annals of Global Analysis and Geometry
Digital Object Identifier (DOI)
Milatovic, O. (2019) The M-Accretivity of Covariant Schrodinger Operators with Unbounded Drift. Annals of Global Analysis and Geometry, 55(4), 657-679.