共查询到17条相似文献,搜索用时 93 毫秒
1.
Trench在[Characterization and properties of (R,S_σ)-commutative matrices,Linear Algebra Appl.,2012,436:4261-4278]中给出了(R,S_σ)-交换矩阵的定义.本文在此基础上讨论(R,S_σ)-交换矩阵的一般性结构,对给定的矩阵X,Y,B,D,以及线性方程组AX=B,YA=D在(R,S_σ)-交换矩阵集合中的最小二乘问题及最佳逼近问题.细致分析最小二乘(R,S_σ)-交换解和最佳逼近解的具体解析表达式.同时在方程组相容情况下分析(R,S_σ)-交换解存在的充要条件及其具体解析表达式. 相似文献
2.
本文研究了群在von Neumann代数上作用的自由性和遍历性问题.利用投影和群SL2(R)的Iwasawa分解,得到了可数离散群在交换von Neumann代数上作用的自由性的等价刻画,证明了SL2(R)在上半平面H上有理作用导出的SL2(R)在极大交换von Neumann代数A={Mf:f∈L2(H,dxdy/y2)}上的作用α是遍历的,但不是自由的. 相似文献
3.
设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A~2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n0且m≠n,U=[A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零. 相似文献
4.
设σ是环R的一个自同态,δ是R的一个σ-导子.研究斜三角矩阵环Tn(R,α)的强可逆性和(σ,δ)-弱刚性,证明了1)若α是环R的一个刚性自同态,则环R是强可逆环当且仅当Tn(R,α)是强可逆环;2)若α和σ都是环R的刚性自同态,ασ=σα,且R是δ-弱刚性环,则R是(σ,δ)-弱刚性环当且仅当Tn(R,α)是(σ,δ)-弱刚性环. 相似文献
5.
SL(2,R)上的Hardy-Littlewood极大函数 总被引:1,自引:0,他引:1
给出了SL(2 ,R)上的Hardy Littlewood极大函数mf 和局部Hardy Littlewood极大函数mRf 的定义 ,对f∈L1(G) ,我们得到了 | {g∈SL(2 ,R) |mf(g) >λ} |的估计 ,且证明了局部Hardy Littlewood极大函数的弱(1.1)型和强 (p ,p)型 ,p >1. 相似文献
6.
本文研究了n维复形上(m,n)-树的判定性质,并对(m,n)-树的-个充分必要条件进行了推广. 相似文献
7.
引入了(I,K)-(m,n)-内射环的概念,给出了(I,K)-(m,n)-内射环的等价刻划.讨论了(I,K)-(m,n)-内射环与(I,K)-(m,1)-内射环之间的关系及左(I,K)-(m,n)-内射环和右(I,K)-(m,n)-内射环的关系.证明了R是右(I,K)-(m,n)-内射环当且仅当如果z=(m1,m2,…,mn)∈Kn且A∈Im×n,rR(A)∈rRn(z),则存在y∈Km,使得z=yA推广了已知的相关结论. 相似文献
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通过引进(m,n)-洞的概念,推广了已有的结论,得到了(m,n)-树的一个新的充分必要条件. 相似文献
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该文借助于犛犔(2,犚)上李代数及其万有包络代数讨论了犛犔(2,犚)上函数的Fourier变换在无穷远处下降的阶与函数的光滑性的关系,我们得到的结论较[6]中的结论好,并由此得到犆2犮(犌)中的Plancherel定理. 相似文献
12.
Benoît Kloeckner 《Geometriae Dedicata》2006,117(1):161-180
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it
is known that there exists countably many analytic equivariant compactification of the isometric action on the hyperbolic
plane. In this paper we study the algebraicity of these actions. We get a classification of the algebraic actions of SL(2,R)
on surfaces. In particular, we classify the algebraic equivariant compactifications of the hyperbolic plane.
An erratum to this article can be found at 相似文献
13.
Benoît Kloeckner 《Geometriae Dedicata》2007,125(1):253-270
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it
is known that there exists countably many analytic equivariant compactification of the isometric action on the hyperbolic
plane. In this paper we study the algebraicity of these actions. We get a classification of the algebraic actions of SL(2;R)
on surfaces. In particular, we classify the algebraic equivariant compactifications of the hyperbolic plane.
The online version of the original article can be found under doi:
. 相似文献
14.
Jianxun He 《Applicable analysis》2013,92(2):495-512
Let SL (2, C ) be the special linear group of 2 ‐ 2 complex matrices with determinant 1 and SU (2) its maximal compact subgroup. Then SL (2, C )/ SU (2) can be realized as the quaternionic upper half-plane $ {\cal H}^c $ . Let SL (2, C ) = NASU (2) be the Iwasawa decomposition and M the centerlizer of A in SU (2). Then P = NA and P a = NAM are the automorphism groups of $ {\cal H}^c $ . In this article, we define the unitary representations of P and P a on L 2 ( C , H ; dz ). From the viewpoint of square integrable group representations we discuss the wavelet transforms, and obtain the orthogonal direct sum decompositions for the function spaces $ L^2({\cal H}^c, \fraca {(dz\, d\rho)}{\rho ^3}) $ and $ L^2({\bf R}^2\times {\bf R}^2, \fraca {dx\, dy\, dx^{\prime }dy^{\prime }}{{({x^{\prime }}^2 + {y^{\prime }}^2)^{\fraca {3}{2}})}} $ . 相似文献
15.
For a given finite index subgroup \(H\subseteq \mathrm {SL}(2,\mathbb {Z})\), we use a process developed by Fisher and Schmidt to lift a Poincaré section of the horocycle flow on \(\mathrm {SL}(2,\mathbb {R})/\mathrm {SL}(2,\mathbb {Z})\) found by Athreya and Cheung to the finite cover \(\mathrm {SL}(2,\mathbb {R})/H\) of \(\mathrm {SL}(2,\mathbb {R})/\mathrm {SL}(2,\mathbb {Z})\). We then use the properties of this section to prove the existence of the limiting gap distribution of various subsets of Farey fractions. Additionally, to each of these subsets of fractions, we extend solutions by Xiong and Zaharescu, and independently Boca, to a Diophantine approximation problem of Erd?s, Szüsz, and Turán. 相似文献
16.
高维Klein群的一个不等式及其应用 总被引:2,自引:0,他引:2
本文首先得到了SL(2,Гn)中Klein群的一个不等式,并给出了它的两个应用;然后证明了对SL(2,Гn)中的非初等群G,若G中的任意斜驶元素f满足tr^2(f)〉4且当∞ 不属于fix(f)时tr(f)=tr(f),则存在h∈SL(2,Гn)使得hGh^-1属于SL(2,R),此结果是Maskit相关结果的推广。 相似文献
17.
AN ASYMPTOTIC ORDER OF FOURIER TRANSFORM ON SL(2,R) 总被引:1,自引:0,他引:1
In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application. 相似文献