Curious properties of canonical divisors in weighted Bergman spaces

Solution of Extremal Problems in Bergman Spaces Using the Bergman Projection

In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical divisors for certain values of $p$.

拟射影流形上Cheng-Yau度量的Bergman核

Bergman Kernels of the Cheng-Yau metrics on quasi-projective manifolds

该研究探讨拟射影流形上Cheng-Yau度量的Bergman核在无穷远光滑除子附近的渐近性，发现近除子点存在量子现象，丰富了复几何与度量几何的相关理论。

加权Bergman空间再生核的一个表示

A representation for the reproducing kernel of a weighted Bergman space

本文针对单位圆盘上由Blaschke因子幂乘积的模构成的权函数，给出了加权Bergman空间再生核的典范表示，并由此推导出有限零点集对应的压缩零除子公式。

On the concept of inner function in Hardy and Bergman spaces in multiply connected domains

We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in $\mathbb{C}$, giving a historical overview and comparing several possible definitions. We explore connections between inner functions, zero-divisors for Hardy spaces and Bergman spaces, and weighted reproducing kernels. After recording some obstructions and negative results, we suggest avenues for further research and point out several open problems.

Zeros of functions in Bergman-type Hilbert spaces of Dirichlet Series

For a real number $α$ the Hilbert spaces $\mathscr{D}_α$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^α< \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_α$ to the case $α>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\mathscr{H}^p$, for $1\leq p <2$.

环域上Hardy空间与Bergman空间上Toeplitz算子的零积问题

Zero Products of Toeplitz operators on the Hardy and Bergman spaces over an annulus

本文研究环域上Hardy与Bergman空间中Toeplitz算子的零积问题，在符号傅里叶展开条件下证明无零因子，并借助Abrahamse约化定理刻画紧Hankel算子，得出零积结果。