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数学学院、所2020年系列学术活动(第249场):余佳洋 博士 四川大学

发表于: 2020-10-19   点击: 

报告题目:L^2 methods in infinite dimensional spaces

报 告 人:余佳洋博士 四川大学

报告时间:2020 年10月23日 15:00-16:00

报告地点:腾讯会议ID:  679 743 967 会议密码:9896

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https://meeting.tencent.com/s/76IUeATL9mjF

校内联系人:朱森  zhusen@jlu.edu.cn


报告摘要:

       The classical L^2 estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a longstanding unsolved problem, due to the essential difficulty that there exists no nontrivial translation invariance measure in the setting of infinite dimensions. The main purpose in this series of work is to give an affirmative solution to the above problem, and apply the estimates to the solvability of the infinite dimensional $\overline{\partial}$ equations. In this first part, we focus on the simplest case, i.e., L^2 estimates and existence theorems for the $\overline{\partial}$ equations on the whole space of $\ell^p$ for $p\in [1,\infty)$. The key of our approach is to introduce a suitable working space, i.e., a Hilbert space for (s,t)-forms on $\ell^p$ (for each nonnegative integers s and t), and via which we define the $\overline{\partial}$ operator from (s,t)-forms to (s,t+1)-forms and establish the exactness of these operators, and therefore in this case we solve a problem which has been open for nearly forty years.


报告人简介:

余佳洋,2014年博士毕业于复旦大学数学科学学院, 现为四川大学数学学院讲师。近年来主要致力于无穷维数学的研究, 最近在无穷维d-bar方程的研究方面取得重要进展。主持国家自然科学基金青年基金项目《算子Lehmer问题与单位球面上的Mahler测度》,参与国家自然科学基金重点项目《随机分布参数系统控制理论》。在TAMS, Illinois J. Math等杂志发表论文。