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1.
通过建立Heisenberg群上无穷远处的集中列紧原理, 研究了如下$p$ -次Laplace方程 -ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u,在Hn上, u∈ D1, p(Hn), 其中ξ∈Hn,λ∈R,1j, 且m, j为整数.  相似文献   

2.
王正栋 《中国科学A辑》1997,40(8):680-684
紧流形M上的以向量场X为漂移项的Brown运动{xt}t≥0可以提升到M×Tk上的一个扩散过程{-xt}t≥0(相应于一个M上的Rk值光滑微分1形式A)。研究提升过程{-xt}t≥0绕环面Tk的k个圈的环流(即旋转数)。适当地选取Rk值微分1形式A。这些环流分别给出了{-xt}t≥0的隐环流和{-xt}t≥0绕M上某些闭圈的旋转数(这些闭圈生成M的一阶同调群H1(M,Z))。  相似文献   

3.
设T ={tj} j∈Z为实序列 ,使得 {eitjξ} j∈Z构成L2( [-π ,π])的一个Riesz基 .设S2m(T ,R)∩L2 (R)是以T ={tj} j∈Z为非正规节点系的多项式缓增样条函数空间 .证明了S2m(T ,R)∩L2 (R)上的Marcinkiewicz Zygmund和Bernstein不等式 .并由此证得渐近关系:E(f,Bπ ,2 ) 2 =limm→∞ E(f,S2m(T ,R) ∩L2 (R) )2 ,其中Bπ ,2 表示L2 (R)中指数≤π的整函数 ,即经典的Paley-Wiener类 .  相似文献   

4.
严子谦 《中国科学A辑》1987,30(12):1233-1244
在可控和自然增长条件下,非线性抛物组 u''t-DaAia(x,t,u,Du)= Bi(x,t,u,Du),i=1,…,N,(x,t)∈Q之解。u∈L2(0,T;H1(Ω,RN))∩L(0,T;L2(Ω,RN))(或∩L(Q,RN))的空间导数Dau事实上属于Llocp(Q,RN),p>2;拟线性抛物组 u''t-Dα[Aijαβ(x,t,u)Dβuj+aja(x,t,u)]=Bi(x,t,u,Du),i=1,…,N的每一个解都在一开集 Q1?Q上 Holder连续,且Hn+2-p(Q\Q1)=0;若当j>i时Aijαβ=0,且Bi(x,t,u,p)关于|p|的增长阶小于2,则Q1=Q;若Aijαβ和aia都Holder连续,则Dau也在Q1上 Holdler连续.  相似文献   

5.
多元Szász—Mirkjan算子的一致逼近   总被引:2,自引:0,他引:2  
本文研究了多元Szása—Mirakjan算子在C2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C2B(T),0a) ;(ii)‖Sn,m(f)-f‖=0(n-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖=0(t<  相似文献   

6.
给出H2(Bn)上复合算子具有闭值域的特征,讨论了Toeplitz算子与复合算子的Fredholm性质。  相似文献   

7.
《数学物理学报(A辑)》2009,29(6):1634-1641
设φ 是Cn的开单位多圆盘上的全纯自映射,α > 0. 该文主要研究了多圆盘上的H与广义加权Bloch空间Bαlog(Un)之间的复合算子Cφ的有界性与紧性.  相似文献   

8.
黄沙 《中国科学A辑》1996,39(3):227-236
讨论Clifford分析中的双正则函数,研究它的Coxo-Plemelj公式和一个非线性边值问题:A(t1,t2++(t1,t2)+B(t1,t2+-(t1,t2)+C(t1,t2-+(t1,t2)+D(t1,t2--(t1,t2)=g(t1,t2)f[t1,t2++(t1,t2),φ+-(t1,t2),φ-+(t1,t2),φ--(t1,t2)].利用积分方程方法和Schauder不动点定理证明了问题解的存在性,并给出了解的积分表示式以及线性情况下解的存在唯一性.  相似文献   

9.
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} ∈VsR, 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   

10.
郑伟安 《中国科学A辑》1981,24(10):1201-1209
本文利用一种特殊的时间变换方法,推广了文献[1]中结果。指出对任何非负局部下鞅(Xt,yt|X|)都存在某个相应的局部鞅(Mt,yt|M|),使得(|Mt|)与(Xt)分布相同。  相似文献   

11.
Let B0^H = {B0^H(t),t ∈ R+^N) be a real-valued fractional Brownian sheet. Define the (N,d)- Gaussian random field B^H by
B^H(t) = (B1^H(t),...,Bd^H(t)) t ∈ R+^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].  相似文献   

12.
Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H n , n > 2. For ν > 0, the Brownian bridge B (ν) of length ν on H is the process B t , 0 ≤t≤ν, conditioned by B 0 = B ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge on ℝ3). The same result holds for the simple random walk on an homogeneous tree. Received: 4 December 1998 / Revised version: 22 January 1999  相似文献   

13.
In this paper we consider the asymptotic behavior of functionals of processes of the form 0 t u s dB s H , where B H is a fractional Brownian motion with Hurst parameter H, and u is a process with finite q-variation, q<1/(1−H). We establish the stable convergence of the corresponding fluctuations.  相似文献   

14.
We consider different types of processes obtained by composing Brownian motion B(t), fractional Brownian motion B H (t) and Cauchy processes C(t) in different manners. We study also multidimensional iterated processes in ? d , like, for example, (B 1(|C(t)|),…, B d (|C(t)|)) and (C 1(|C(t)|),…, C d (|C(t)|)), deriving the corresponding partial differential equations satisfied by their joint distribution. We show that many important partial differential equations, like wave equation, equation of vibration of rods, higher-order heat equation, are satisfied by the laws of the iterated processes considered in the work. Similarly, we prove that some processes like C(|B 1(|B 2(…|B n+1(t)|…)|)|) are governed by fractional diffusion equations.  相似文献   

15.
16.
Let ξA,B be the Krein spectral shift function for a pair of operatorsA, B, with C =A-B trace class. We establish the bound
whereF is any non-negative convex function on [0, ∞) with F(0) = 0 and Ώj (C) are the singular values ofC. The choice F(t) =t p ,p ≥ 1, improves a recent bound of Combes, Hislop and Nakamura. Supported in part by NSF grant DMS-9707661.  相似文献   

17.
Consider an initial Lagrangian submanifold Λ0T* ℝ n that admits a global generating function and a Hamiltonian isotopy Φ H t . Then, we provide a global generating function for the Lagrangian submanifold Λ t = Φ H t 0) realized by applying the so-called Amann-Conley-Zehnder reduction. When Λ0 is the zero-section, we study in some detail the asymptotic behavior of such generating functions and give an approximation result. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.  相似文献   

18.
Whenϕ is an analytic map of the unit diskU into itself, andX is a Banach space of analytic functions onU, define the composition operatorC ϕ byC ϕ (f)=f o ϕ, forfX. In this paper we show how to use the Calderón theory of complex interpolation to obtain information on the spectrum ofC ϕ (under suitable hypotheses onϕ) acting on the Bloch spaceB and BMOA, the space of analytic functions in BMO. To do this we first obtain some results on the essential spectral radius and spectrum ofC ϕ on the Bergman spacesA pand Hardy spacesH p,spaces which are connected toB and BMOA by the interpolation relationships [A 1,B] t =A pand [H 1,BMOA] t =H pfor 1=p(1−t).  相似文献   

19.
Let {BH1,H2(t1,t2),t1?0,t2?0} be a fractional Brownian sheet with indexes 0<H1,H2<1. When H1=H2:=H, there is a logarithmic factor in the small ball function of the sup-norm statistic of BH,H. First, we state general conditions (one based on a logarithmic factor in the small ball function) on some statistics of BH,H. Then we characterize the sufficiency part of the lower classes of these statistics by an integral test. Finally, when we consider the sup-norm statistic, the influence of the log-type small ball factor in the necessity part is measured by a second integral test.  相似文献   

20.
The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes BH={BH(t)}tRBH={BH(t)}tR by allowing their self-similarity parameter H∈(0,1)H(0,1) to depend on time.  相似文献   

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