刘华教授学术报告

发布时间:2018年03月14日 作者:唐颖   消息来源:业务办    阅读次数:[]

报告题目: Hilbert Transformation and $r\mathrm{Spin}(n)+\mathbb{R}^n$ Group 报告人: 刘华 教授,天津职业技术师范大学 报告时间: 2018年3月19日下午2:30-3:30(星期一) 报告地点: 数学院一楼145报告厅 报告摘要: In this paper we study symmetry properties of the Hilbert transformation of several real variables in the Clifford algebra setting. In order to describe the symmetry properties we introduce the group $r\mathrm{Spin}(n)+\mathbb{R}^n, r>0$, which is essentially an extension of the ax+b group.The study concludes that the Hilbert transformation has certain characteristic symmetry properties in terms of $r\mathrm{Spin}(n)+\mathbb{R}^n$. In the present paper, for $n=2$ and $3$ we obtain, explicitly,the induced spinor representations of the $r\mathrm{Spin}(n)+ \mathbb{R}^n$ group.Then we decompose the natural representation of $r\mathrm{Spin}(n)+\mathbb{R}^n $ into the direct sum of some two irreducible spinor representations, by which we characterize the Hilbert transformation in $\mathbb{R}^3$ and $\mathbb{R}^2$. Precisely, we show that a nontrivial skew operator is the Hilbert transformation if and only if it is invariant under the action of the $r\mathrm{Spin}(n)+\mathbb{R}^n, n=2,3,$ group.



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