讲座题目：Random Hardy Shift
报告人：方向 教授
主持人：吉国兴 教授
活动时间：15:00
地点：长安校区 数学与信息科学学院学术交流厅
主办单位：数学与信息科学学院
讲座内容简介：
This talk seeks to answer basic questions concerning the random counterpart of the unilateral shift, a.k.a. the Hardy shift. It is well known that, on finite dimensional vector spaces, random matrix theory has evolved into a sophisticated subject. On infinite dimensional spaces, there are some works on random operators, but mostly restricted to the self-adjoint and unbounded case, such as random Schrodinger operators. A random theory for non-self-adjoint operators acting on infinite dimensional spaces is largely missing so far. We seek to develop such a theory by first considering the simplest non-selfadjoint operator: the unilateral shift. It is defined as
$$Te_n=e_{n+1}, \quad n=1, 2, \cdots,$$
where $\{e_n\}_{n=1}^\infty$ is an orthonormal basis for a separable complex Hilbert space. We consider the random counterpart: Namely,
$$Te_n=X_ne_{n+1}, \quad n=1, 2, \cdots,$$
where $\{X_n\}_{n=1}^\infty$ is a sequence of i.i.d. random variables. We propose to study it in parallel to the three well known shfits (Hardy, Bergman, and Dirichlet).
讲座人简介：
方向，台湾中央大学教授。研究兴趣为泛函分析和随机分析。
