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

2019/04/11 by Saratchandran, Hemanth
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1904.07210

Abstract

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.

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