The Problem of Limits on a Riemannian Manifold

Abstract

The object of this note is to study the self-adjoint extensions of the Laplace operator, defined on the space of C^∞ forms with compact support, in the Hilbert space of square summable forms on aC^∞ Riemannian manifold, by using the theory of currents and the theory of linear transformations on a Hilbert space.