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Estimate of the $L^p$-Fourier Transform Norm on Strong *-Regular Exponential Solvable Lie Groups
Exponential Lie group Plancherel measure unitary representation coadjoint orbit $L^p$-Fourier transform
2007/12/13
We study the $L^{p}$-Fourier transform for a special class of exponential Lie groups, the strong $\ast$-regular exponential Lie groups. Moreover, we provide an estimate of its norm using the orbit met...
本文讨论了紧李群上Fourier级数的方体平均求和的几乎处处收敛问题,并用这一结果,讨论了多复变数典型域$R_1$上Cauchy型积分的边界性质与Dirichlet问题.
紧李群上 Fourier 系数的渐近性质
2007/12/12
本文证明了,若 G 是非交换的紧李群(交换的紧李群必是 n维环群),则仅当$f\in L^2(G)$时,才成立着关于 Fourier 系数的Riemann-Lebesgue 引理.而对$L^p(G),1\leq p<2$,则存在着 Fourier系数发散于无穷的函数.且 p不同时,$L^p(G)$中“最坏的”函数发散于无穷的阶均不相同,本文给出了阶的精确估计.
用两单参数李群求$3$阶自治系统的首次积分
$3$阶自治系统 首次积分 单参数李群
2007/12/10
在较一般的条件下, 对$3$阶自治系统给出利用系统所接受的两个 单参数李群的生成元计算首次积分的方法.
Finitary Actions and Invariant Ideals
group algebra invariant ideal locally finite simple group finitary permutation group permutation module finitary linear group
2010/2/26
Let K be a field and let G be a group. If G acts on an abelian group V, then it acts naturally on any group algebra K[V], and we are concerned with classifying the G-stable ideals of K[V]. In this pap...
Linear Automorphism Groups of Relatively Free Groups
Linear Automorphism Groups Relatively Free Groups
2010/2/26
Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group...