Mathematical Sciences: Pointwise Convergence of Operators, Classification of Nonsingular Transformation

阿萨尼教授的研究将集中在三个问题上。 它们与算子理论、遍历理论和 谐波分析 （一）是否可以推广最近的成果 关于动力系统返回到 算子理论背景 II）光谱表征 的近似传递性属性引入的Connes和 能得到树林吗？ III）哪些类型的运算符具有迭代 当作用于一个函数时几乎处处收敛 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 现代理论认为， 变换作用于光滑空间。 此外，遍历理论 与算子理论和谐波分析接触时， 动态包括再次应用单个变换， 再

Professor Assani's research will focus on three problems. They are connected to operator theory, ergodic theory, and harmonic analysis. I) Is it possible to extend the recent result of J. Bourgain on the return times of dynamical systems to an operator theoretic context? II) Can a spectral characterization of the approximate transitivity property introduced by Connes and Woods be obtained? III) What kinds of operators have iterates which when acting on a function converge almost everywhere? This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In addition ergodic theory makes contact with operator theory and harmonic analysis when the dynamics consists of applying a single transformation again and again.