Self-adjoint extensions of differential operators on Riemannian manifolds
We study (Formula presented.), where D is a first order elliptic differential operator acting on sections of a Hermitian vector bundle over a Riemannian manifold M, and V is a Hermitian bundle endomorphism. In the case when M is geodesically complete, we establish the essential self-adjointness of positive integer powers of H. In the case when M is not necessarily geodesically complete, we give a sufficient condition for the essential self-adjointness of H, expressed in terms of the behavior of V relative to the Cauchy boundary of M.
Annals of Global Analysis and Geometry
Digital Object Identifier (DOI)
Milatovic, & Truc, F. (2015). Self-adjoint extensions of differential operators on Riemannian manifolds. Annals of Global Analysis and Geometry, 49(1), 87–103. https://doi.org/10.1007/s10455-015-9482-0