Dynamical properties in weighted Orlicz spaces on tree
数学学科创建110周年系列报告
报告题目(Title)：Dynamical properties in weighted Orlicz spaces on tree
报告人(Speaker)：龙品红（宁夏大学）
地点(Place)：腾讯会议379 317 656 密码794716
时间(Time)：2025年11月28日（周五）10:00-11:00
邀请人(Inviter)：高志强
报告摘要
The linear dynamics combine the classically topological dynamics with functional analysis and operator theory. In this field the key topic is to study some problems which are related to the density of orbits for linear bounded operators. In this talk, we mainly discuss the dynamical theories for shifts in weighted Orlicz spaces on directed tree. Firstly, we generalize Orlicz spaces to weighted Orlicz spaces on tree and give some related properties. Secondly, in the tree setting we provide some sufficient or necessary conditions for boundedness of backward and forward shift operators, and the equivalency of ones to be hypercyclic and weak mixing on Orlicz spaces. Thirdly, we also obtain several equivalent conditions for backward shift operators to be F-transitive in Orlicz spaces on directed rooted and unrooted trees. Fourthly, we show several equivalent conditions for backward shift operators to be F-supercyclic in Orlicz spaces on directed trees, and meanwhile characterize the hypercyclicity of backward shift with respect to limit points. Finally, we give sufficient conditions for backward shift operators to be frequently hypercyclic in Orlicz spaces on unrooted directed trees.
主讲人简介
龙品红，任职于宁夏大学数学统计学院，副教授，硕士生导师，博士毕业于北京师范大学，其研究兴趣为复分析、广义函数空间的不动点理论、变指数函数空间、位势理论与线性算子动力系统等领域泛函或算子刻画及应用. 目前为止, 已经在JMAA、JNSNS、 NYJM、数学年刊、数学物理学报等学术期刊上发表学术论文 40 余篇，已主持国家自然科学基金项目1项和宁夏自然科研基金以及宁夏高校项目多项。
