We consider perturbed quadharmonic operators, ${\mathrm{\Delta }}^4+V$, 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 L² when the perturbed operator acts on functions.

中文翻译：

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黎曼流形上摄动四调和算子的基本自伴性及其在分离问题上的应用

我们考虑扰动的四谐波算子， ${\mathrm{\Delta }}^4+\mathrm{伏特}$，作用在一个完整的黎曼流形上的埃尔米特向量束的各部分上，势V满足从下到下的一个非正函数（取决于到点的距离）的范围。在关于Hermitian向量束和底层黎曼流形的有界几何假设下，我们为此类算子的基本自伴性提供了充分条件。然后，当扰动算子作用于函数时，我们将其用于证明L ^2中的分离性质。