報告題目：L^2 methods in infinite dimensional spaces
報 告 人：餘佳洋博士 四川大學
報告時間：2020 年10月23日 15：00-16：00
報告地點：騰訊會議ID: 679 743 967 會議密碼：9896
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校内聯系人：朱森 zhusen@jlu.edu.cn
報告摘要：
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.
報告人簡介：
餘佳洋，2014年博士畢業于複旦大學數學科學學院, 現為四川大學伟德线上平台講師。近年來主要緻力于無窮維數學的研究, 最近在無窮維d-bar方程的研究方面取得重要進展。主持國家自然科學基金青年基金項目《算子Lehmer問題與單位球面上的Mahler測度》，參與國家自然科學基金重點項目《随機分布參數系統控制理論》。在TAMS, Illinois J. Math等雜志發表論文。
