论文标题
高斯曲率与Cowen-Douglas操作员的曲率的关系
The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator
论文作者
论文摘要
最近已经显示，如果$ k $是sesqui分析标量，对域中的$ \ mathbb c^m $的$ω$具有无负的确定内核，则该功能$ \ big（k^2 \ partial_i \ bar {\ bar {\ partial} $ω$的内核。在本文中，我们讨论了这一结果的两个后果。第一个增强了Cowen-Douglas类$ B_1（ω）$中运算符的曲率不平等，而第二个则给出了某些希尔伯特模块的子模块的复制核与相关商模块的曲率的关系。
It has been recently shown that if $K$ is a sesqui-analytic scalar valued non-negative definite kernel on a domain $Ω$ in $\mathbb C^m$, then the function $\big(K^2\partial_i\bar{\partial}_j\log K\big )_{i,j=1}^ m,$ is also a non-negative definite kernel on $Ω$. In this paper, we discuss two consequences of this result. The first one strengthens the curvature inequality for operators in the Cowen-Douglas class $B_1(Ω)$ while the second one gives a relationship of the reproducing kernel of a submodule of certain Hilbert modules with the curvature of the associated quotient module.
