Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-02-20 , DOI: 10.1016/j.jat.2020.105391 S. Charpentier
We are interested in functions analytic in the unit disc of the complex plane with a wild behaviour near the boundary of . For instance, the main result implies the existence of a residual subset of every element of which satisfies the property that, given any compact subset of , different from , any continuous function on , and any compact set of , there exists an increasing sequence converging to 1, such that converges to , uniformly for , as goes to . Among other things, radial growth of such functions and connections with universal Taylor series are investigated. Functions in the disc algebra whose derivatives disjointly satisfy a somewhat similar universal property, are also exhibited. In some sense, the results are sharp.
中文翻译:
具有通用边界行为的全纯函数
我们对单元盘中的功能分析感兴趣 边界附近具有狂野行为的复杂平面 的 。例如,主要结果意味着存在一个残差子集 每个元素 给定紧凑的子集,其中的一个满足 的 , 不同于 ,任何连续函数 上 ,以及任何紧凑套装 的 ,存在一个增加的序列 收敛到1,这样 收敛到 ,统一用于 ,作为 去 。其中,研究了这种函数的径向增长以及与通用泰勒级数的联系。还显示了圆盘代数中的函数,它们的导数不相交地满足了某种相似的通用性。从某种意义上讲,结果是清晰的。