广义Neil抛物线上的不变度量和不变距离

Function theory on the Neil parabola

We give a formula for the Carathéodory distance on the Neil parabola, the variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety with a singularity to have its Carathéodory distance explicitly computed. In addition, we relate this to a mixed Carathéodory-Pick interpolation problem for which known interpolation theorems do not apply. Finally, we prove a bounded holomorphic function extension result from the Neil parabola to the bidisk.

解析函数空间上的自同构与广义投影

Automorphisms and generalized projections on spaces of analytic functions

本文对开单位圆盘上有界解析函数的两个闭子代数（包括Neil代数）的自同构进行了完整分类，并刻画了$H^{p}(\mathbb{D})$和$H^{p}(\mathbb{D}^2)$（$1\leq p \leq \infty$，$p\neq 2$）上的广义三圆投影。