【廿周年院庆学术报告10】 · 【和山数学论坛第318期】
一、报告题目：Analytic automorphism group and similar representation of Analytic functions
二、报告人：蒋春澜 教授
三、时 间：2022年9月16日(周五) 下午 14:30-15:30
四、腾讯会议号：582 240 462
报告摘要： In geometry group, one of the milestone is M. Gromov’s polynomial growth theorem: Finitely generated groups have polynomial growth if and only if they are virtually nilpotent. In the paper, we introduce the growth types of weighted Hardy spaces, which are inspired by M. Gromov’s work, and we give the Jordan representation theorem for the analytic function on the unit closed disk as multiplication operators on a weighted Hardy spaces of polynomial growth. In particular, on a weighted Hardy space of polynomial growth, the multiplication operators 
is similar to 
for analytic automorphism 
on the unit open disk, and for any Blaschke product B of order m, 
is similar to 
which is an affirmative answer to a generalized version of a question raised by R. Douglas in 2007. By the way, we also give a counterexample to show that could be not similar to on a weighted Hardy space of intermediate growth.
报告人简介：蒋春澜，河北师范大学教授，博士生导师, 省管专家，河北省燕赵学者。曾任河北师范大学校长、中国科学院访问教授、美国波多黎哥大学客座教授、国家自然科学基金委员会学科评议组专家。长期从事算子代数可约性与强不可约性研究。在无穷维希尔伯特空间算子理论中作出了享有国际声誉的贡献，在PNAS、Adv. Math.、J. Funct. Anal.、Trans. Amer. Math. Soc.、IMRN等杂志发表学术论文70多篇。主持完成《国家重点基础研究发展规划》（973计划）项目、教育部重大课题、国家自然科学基金面上项目十余项，正在主持国家基金委重点基金项目1项。曾获国家教委科技进步二等奖、上海市科技进步二等奖。2000年获国务院政府特殊津贴，2003年获河北省自然科学一等奖，2013年获教育部自然科学二等奖。
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