报告摘要：The theory of Bergman spaces has, in the past several decades, become important in complex analysis of both one and several complex variables. When $p=2$, the reproducing kernel plays an important role in the Hilbert space. For the classical Bergman spaces the reproducing properties and biholomorphic invariance are investigated. Bergman kernels have also been considered in some weighted cases.

Since a reproducing kernel deliveries certain fundamental information of the corresponding space, it is important to obtain the concrete form of the kernel function.

However, we must confess that their weighted Bergman kernel can almost never be calculated explicitly except for some special cases.

However, for unbounded regions, density of polynomials can not be guaranteed. In this case, appropriate weight functions are introduced such that the weighted polynomials are dense in Bergman spaces on unbounded domains. Then the kernel representation can be similarly obtained. In this paper, we apply the Laplace transform to the case of Bergman spaces on tube domains, which will be a good new method to calculate reproducing kernels.

个人简介：邓冠铁,北京师范大学二级教授，博士生导师，数学科学学院特聘教授，俄罗斯“UFA Mathematical Journal”数学杂志编委. 曾任“Frontiers of Mathematics in China” 杂志编委.邓冠铁出版研究生教材”复分析”和本科生教材“复变函数论”,出版专著两部.

报告时间：2025年6月7日8：30 -11：30

报告地点：北衡楼1420