Essential self‐adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problem

We consider perturbed quadharmonic operators, Δ4+V, acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non‐positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vector bundle and the underlying Riemannian manifold, we give a sufficient condition for the essential self‐adjointness of such operators. We then apply this to prove the separation property in L2 when the perturbed operator acts on functions.