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【數學學院】9.29 The Kozlov completeness problem

  • 日期:2019-09-23        來源:四川大學數學學院         點擊數:

報告題目:The Kozlov completeness problem

報告人:郭坤宇 (復旦大學數學科學學院教授)

報告時間:2019年9月29日  下午16:00-17:00


報告摘要: The classical completeness problem raised by Beurling and       independently by Wintner asks for which $\psi\in L^2(0,1)$, the dilation      system $\{\psi(kx):k=1,2,\cdots\}$ is complete in $L^2(0,1)$, where $\psi$  is identified with its extension to an odd $2$-periodic function on $\mathbb{R}$. This difficult problem is nowadays commonly called as the Periodic Dilation Completeness Problem (PDCP). When $0<s\leq 1$, let $\chi_s$ be the characteristic function of $[0,s]$, and $\mathcal{D}_s=\{\chi_s(kx):k=1,2,\cdots\}$. The Kozlov completeness problem is to ask for which $s$, the dilation system $\mathcal{D}_s$ is complete. In this talk, we give a brief     introduction for the Periodic Dilation Completeness Problem and the Kozlov completeness problem, and present some significant progress on this topic. This is a joint work with Dr.Dan.



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