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arXiv · 1904.07210

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

Hemanth Saratchandran
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Abstract

We consider perturbed quadharmonic operators, $\Delta^4 + V$, 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 $L^2$ when the perturbed operator acts on functions.

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BibTeXRIS

Hemanth Saratchandran. 2019-04-11. Essential self-adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problem. https://arxiv.org/abs/1904.07210

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