題 目：On the symbol space problem for random analytic functions: some recent results
内容簡介：
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.
報告人：方向
報告人簡介：台灣陽明交通大學教授，2002年博士畢業于美國德州農工大學，主要研究興趣包括函數空間、泛函分析、概率論等。已在Geom. Funct. Anal., J. Reine Angew. Math., Adv. Math., J. Funct. Anal., IMRN, Trans. Amer. Math. Soc., Math. Res. Lett.等頂級數學期刊發表二十餘篇高水平論文。
時間：2024年12月24日 16：00開始
地點：石牌校區南海樓224室
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