:::

學術專區

:::
演講
活動開始時間2018-10-15 16:00:00
活動結束時間2018-10-15 17:00:00
活動名稱學術演講-Random Weighted Shifts
主講者方向 教授 (國立中央大學)
活動地點綜合三館4F Lecture Room B
活動內容點選觀看
附件檔案 檔案下載 Adobe PDF
參考連結 
備註Abstract
This talk represents some of our initial efforts to develop
what we call a non-selfadjoint version of random operator theory. It is well known that, on finite dimensional vector spaces, random matrix theory has evolved into a remarkably sophisticated subject. On infinite dimensional spaces, most works on random operators so far are restricted to the selfadjoint case, such as random Schrodinger operators. A non-selfadjoint theory is largely missing so far. We
seek to understand the random counterpart of a canonical
non-selfadjoint operator, namely, the unilateral shift, 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. This seemingly naive operator encompasses a broad range of beautiful theorems, especially in its connection to complex analysis. Our goal is to consider its random counterpart:

$$Te_n=X_ne_{n+1}, \quad n=1, 2, \cdots,$$

where $\{X_n\}_{n=1}^\infty$ is a sequence of i.i.d. random variables.
This clearly fundamental model seems to elude investigation in the literature so far.
最後更新日期2018-10-01 09:42:39
20161228
cron web_use_log