報告題目：Atomic decomposition of noncommutative martingales

報 告 人： 吐爾德别克 教授

時   間：2024年6月17日上午10:00—12:00

地   點： 伟德国际1916备用网址602

報告摘要：Atomic decomposition plays a fundamental role in the classical martingale theory and harmonic analysis. For instance, atomic decomposition is a powerful tool for dealing with duality theorems, interpolation theorems and some fundamental inequalities both in martingale theory and harmonic analysis. Atoms for martingales are usually defined in terms of stopping times. Unfortunately, the concept of stopping times is, up to now, not well-defined in the generic noncommutative setting (there are some works on this topic, for example,see the works of Attal and Coquio). We note, however, that atoms can be defined without help of stopping times. In this talk, we show that the atomic decomposition for the Hardy spaces h1 and H1 is valid for noncommutative martingales. We also present recent results on atomic decomposition.

報告人簡介：吐爾德别克，阿斯塔納信息技術大學教授，博士生導師。主要從事非交換鞅、算子函數論、非交換調和分析等領域的研究。主持多項國家自然科學基金項目，出版專著一本，在Trans. AMS, JFA，Math. Z., J. Operator Theory等著名雜志發表學術論文70餘篇。