講座題目：Random Hardy Shift

報(bào)告人：方向 教授

主持人：吉國興 教授

活動(dòng)時(shí)間：15:00

地點(diǎn)：長(zhǎng)安校區(qū) 數(shù)學(xué)與信息科學(xué)學(xué)院學(xué)術(shù)交流廳

主辦單位：數(shù)學(xué)與信息科學(xué)學(xué)院

講座內(nèi)容簡(jiǎn)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).

講座人簡(jiǎn)介：

方向，臺(tái)灣中央大學(xué)教授。研究興趣為泛函分析和隨機(jī)分析。