题 目：On the symbol space problem for random analytic functions: some recent results
内容简介：
Let $f(z)=\sum_{n=0}^\infty a_n z^n$ be an analytic function and let $$Rf(z)= \sum_{n=0}^\infty \pm a_n z^n$$ be its randomization.
Let $E$ be any (Banach) space of analytic functions.Then, under mild conditions, the following probability is either 0 or 1 for any $f$; that is, $P(Rf \in E) \in \{0, 1\}.$
We define the space $E_*$ of random symbols to be $E_*=\{f: Rf \in E almost surely\}$.
The characterization of $(H^p)_*=H^2$, for any $p > 0$, is due to Littlewood in 1930. In this talk, we review the history and report those recently characterized $E_*$, including the Bergman/Dirichlet spaces, Fock spaces, Triebel-Lizorkin/tent spaces, the generalized Nevanlinna class, the generalized Blaschke class, those satisfying a polynomial growth rate in the unit disk, and entire functions with a finite order.
报告人：方向
报告人简介：台湾阳明交通大学教授，2002年博士毕业于美国德州农工大学，主要研究兴趣包括函数空间、泛函分析、概率论等。已在Geom. Funct. Anal., J. Reine Angew. Math., Adv. Math., J. Funct. Anal., IMRN, Trans. Amer. Math. Soc., Math. Res. Lett.等顶级数学期刊发表二十余篇高水平论文。
时间：2024年12月24日 16：00开始
地点：石牌校区南海楼224室
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