论文标题
在封闭的riemannian歧管上，光谱Zeta内核的某些统治不平等
Some domination inequalities for spectral zeta kernels on closed Riemannian manifolds
论文作者
论文摘要
我们首先证明了Kato的Laplacian和Schr $ \ ddot {O} $ Dinger-type操作员在封闭的Riemannian歧管上的平滑功能上的不平等现象。然后，我们将结果应用于光谱ZETA函数及其相关光谱Zeta内核上的一些新的统治不平等，使用Kato的不平等和大量化技术，对$ n $二维单位球体上的Zeta内核。我们的结果是对riemannian表面的比较不平等现象的概括，即$ n $ n $维的封闭式riemannian歧管。
We first prove Kato's inequalities for the Laplacian and a Schr$\ddot{o}$dinger-type operator on smooth functions on closed Riemannian manifolds. We then apply the result to establish some new domination inequalities for spectral zeta functions and their related spectral zeta kernels on $n$-dimensional unit spheres using Kato's inequalities and majorisation techniques. Our results are the generalisations of Kato's comparison inequalities for Riemannian surfaces to $n$-dimensional closed Riemannian manifolds.
