共查询到20条相似文献,搜索用时 78 毫秒
1.
In this paper it is proved that local fundamental solution exists in some space Wm(Hn) (m∈Z), if the left invariant differential operator on the Heisenberg group Hn satisfies certain condition. The main results are:l.Let L be a left invariant differential operator on Hn. If there exist R≥0, r,s∈R and operators {Bλ|λ∈ΓR} ∈Vs(ΓR, Mr) such that, for almost all λ∈ΓR, Bλ is the right inverse of Ⅱλ(L), then there exists E∈Wm(Hn) (when m≥0 or m even) or E∈Wm-1(Hn) (when m<0 and odd) such that LE =δ(near the origie) Where m=min([r],-[2s]-n-2); 2. Let L(W,T) be of the form (3.1). If there exist R≥0 and r,s∈R such that when |λ|≥R,(?) and Cλ≥ C|λ|x(C>0), then the same conclusion as above holds with m=min(-[2r]-n-2,[-2s]-n-2). 相似文献
2.
3.
4.
5.
三角域上Bernstein多项式的Lipschitz常数 总被引:1,自引:0,他引:1
设T是平面上以T1,T2,T3为顶点的三角形,f(p)为定义在T上的函数,称Bn(f,P):=(?)f(i/n,j/n,k/n)Bi,j,kn(P),为f的n次Bernstein多项式,这儿Bi,j,kn(P):(n!)/(i!j!k!)uivjωk是Bernstein基函数,(u,v,w)是P关于T的重心坐标。 B.M.Brown等人对单变量的Bernstein多项式证明了如果f∈LipAλ,0<λ≤1,则对所有的n,都有Bα(f,x)∈LipAλ。本文的目的是对定义在三角域T:{(x,y):x≥0,y≥0,x+y≤1}上的Bernstein多项式证明了类似的结果: 设f(P)∈LipAλ,0<λ≤1,则对所有的n,Bn(f,P)∈Lip(21/2λA)λ,并且,在一定意义上,常数21/2λA是最好的。 上述结果对于任意的锐角或直角三角形T,也是成立的。 最后还指出,当T可为钝角三角形时,则不存在同一常数C,使对所有的n和任意三角形T,有Bn(f,P)∈Lipcλ。 相似文献
6.
两个四元数自共轭半正定矩阵乘积的特征估计 总被引:5,自引:4,他引:1
设A和B均非0的n阶实四元数自共轭矩阵,λi及μi分别为共特征值(i=1,…,n),且规定|λ1|≥|λ2|≥…≥|λn|,|μ1|≥|μ2|≥…≥|μn|,又λ为AB之任意特征值,则λ为实数,且(1)若A≥0,A(?)GLn(Q),B≥0,B GLn(Q),则λ≤λ1μ1;(2)若A>0或B>0,则|λ|≤|λ1μ1|,特别当A>0且B>0时有λ≤λ1μ1;(3)若A>0,B∈GLn(Q),或B>0,A∈GLn(Q)则|λ|≥|λnμn|,特别当A>0且B>0时有λ≥λnμn。 相似文献
7.
利用权函数方法和实分析技巧, 在λ1λ2 > 0 的条件下,讨论具有非齐次核K(n,x)=G(nλ1xλ2)的半离散Hilbert型不等式成立的等价参数条件及最佳常数因子问题, 最后讨论其在算子理论中的应用. 相似文献
8.
设Xn, n≥1是独立同分布正的随机变量序列, E(X1)=u >0, Var(X1)=σ2, E|X1|3<∞, 记Sn==∑Nk=1Xk, 变异系数γ=σ/u.g是满足一定条件的无界可测函数, 证明了
limN→∞1/logN∑Nn=11/n g((∏nk=1Sk/n!un )1/γ√n )=∫∞0g(x)dF(x),a.s.,
其中 F(•) 是随机变量e√2ξ 的分布函数, ξ 是服从标准正态分布的随机变量. 相似文献
9.
10.
设Ω?Rn是一个有界正则区域,{λk}是-△在H0(Ω)上的一列特征值。假定对某个给定的k,λk是单重的,φ为其相应的特征函数,∫φ2=1 固定h∈H-1使∫hφ=0。 相似文献
11.
F. J. Schuurmann P. R. Krishnaiah A. K. Chattopadhyay 《Journal of multivariate analysis》1973,3(4):445-453
In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed. 相似文献
12.
用常微分方程模型分析预防和隔离措施对SARS发病率的影响 总被引:2,自引:2,他引:0
通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 . 相似文献
13.
《European Journal of Operational Research》2005,161(2):377-385
The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model. 相似文献
14.
《Chaos, solitons, and fractals》2001,12(6):1101-1109
Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously. 相似文献
15.
Hans Jürgen Borchers 《Annales Henri Poincare》2002,3(1):1-17
The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m1 there is no gap in the spectrum which is larger than 2m1. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables. 相似文献
16.
Presented by A. F. Pixley. 相似文献
17.
18.
For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues
denote by E(λi; T) the eigen-projection corresponding to an eigenvalue λi. In this paper we will show that if the operator sequence
is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators Tp and Tr: T = Tp + Tr, where Tp is the weak limit of Tn and Tr is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body. 相似文献
19.