论文标题
连续的分析能力和全态运动
Continuous analytic capacity and holomorphic motions
论文作者
论文摘要
我们构建了一个紧凑的集合，其连续的分析能力在一定的全体形态运动下不会连续变化，从而回答了Paul Gauthier的问题。我们的示例灵感来自全体形态动力学，并依赖于主教的作品 - 卡莱森 - 加内特 - 琼斯和眉毛 - 与约旦曲线的切线，谐波测度和迪里奇莱特代数相关的wermer。我们的方法还提供了Ransford，Younsi和AI结果的新证明，涉及全体形态运动下的分析能力的变化。此外，我们表明可能不存在连续分析能力的极端功能。
We construct a compact set whose continuous analytic capacity does not vary continuously under a certain holomorphic motion, thereby answering a question of Paul Gauthier. Our example is inspired by holomorphic dynamics and relies on the works of Bishop--Carleson--Garnett--Jones and Browder--Wermer relating tangent points of Jordan curves, harmonic measure and Dirichlet algebras. Our approach also provides a new proof of a result of Ransford, Younsi and Ai on the variation of analytic capacity under holomorphic motions. In addition, we show that extremal functions for continuous analytic capacity may not exist.
