抽象度量空间上的一致连续函数空间

本文主要讨论抽象度量空间上的一致连续函数空间的Banach空间结构,代数结构和格结构．     

在险风险值估计方法的比较研究

金融数据呈现的厚尾性已达成共识。本文首先基于指数回归模型提出了一种厚尾分布的极值分位数估计方法,得到了在险风险值的估计公式。然后得到了上海上证指数、国债指数和企业债券指数的在险风险值的估计值,比较了他们的极值风险.     

近切触流形的φ*-解析向量场

本文引入了近切触流形（M,ø,ξ,η,g）中φ^*-解析向量场的概念,并研究了其性质.利用近切触流形的性质,证明了切触度量流形中的φ^*-解析向量场v是Killing向量场且φv不是φ^*-解析的.特别地,如果近切触流形M是正规的,得到v与ξ平行且模长为常数.另外,证明了3维的切触度量流形不存在非零的φ^*-解析向量场.     

L~p空间中神经网络逼近的几何速度

该文主要研究了L~p空间中神经网络逼近的几何速度.将凸贪婪迭代法应用于L~p空间中满足"δ-角度的条件"的一类函数.作者将文献的结论推广到L~p空间中,得到当0q1时人工神经网络逼近的速度是o(q~n).     

关于Fermat素数与L-函数的加权均值

本文研究了一类以Fermat素数为模的Dirichlet L-函数加权均值的计算问题. 利用初等方法以及Dirichlet 和的性质, 获得了一个有趣的计算公式.     

关于一类弱Berwald的(α,β)-度量

本文研究了一类重要的形如F=α +εβ +β arctan(β/α) (ε为常数)的弱Berwald (α, β)-度量.利用S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失.     

广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性

本文研究了广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性.利用对函数进行环形分解技术和算子截断的方法,获得了广义分数次积分算子L~(-β/2)(f)从MK_(p,q1)~(α,λ)(ω1,ω_2~(q1))空间到MK_(p,q2)~(α,λ)(ω_1,ω_2~(q2))空间是有界的,从而将分数次积分算子在齐次加权Morrey-Herz空间上的有界性推广到广义分数次积分算子.     

在险值与L~p-空间上的连续一致风险度量（英文）

本文研究了在险值和L~p-空间上的连续一致风险度量之间的关系.利用凸集分离定理和截尾逼近方法,获得了在险值可以用L~p-空间上的连续一致风险度量表示的结果,并且得到了L~p-空间上的表示定理的一种新的证明方法.它们分别是文献[2]的相关结论从L~∞-空间到L~p-空间上的推广和对Inoue~[4]做的一些补充证明.     

l p值Gauss过程的增量有多大

设{Y(t),t≥0}={X_k(t),t≥0}^∞_k=1是独立的Gauss过程序列,σ²_k(h)=E(X_k(t+h)-X_k(t))².记σ(p,h)=(sum from k=1 to ∞ σ^p_k(h))^1/p,P≥1.考察σ(P,h)有界时Y(·)的大增量.作为一个例子,给出了无穷维分数Ornstein-Uhlenbeck过程在l^p空间中的大增量.所建立的方法适用于某些其它类型的平稳增量过程.     

Fock-Sobolev空间上有界、紧与S_p-类算子

本文研究Fock-Sobolev空间上稠密定义算子,将这些算子统一表示成积分算子,利用积分算子的方法得到了它们的一个充分条件,并构造反例说此充分条件是非必要的,还得到这些算子为紧算子的两个充分条件.最后构造符号函数在复平面上每一点处本性无界的紧和Sp-类(0p∞)Toeplitz算子.     

关于L_p球的几个新不等式和性质(英文)

本文研究了L_p球的相关问题.利用对偶混合体积、球面Radon变换和Fourier变换的方法,获得了关于L_p球的几个新不等式和性质,其中一个不等式与著名的最大切片猜想有关.     

Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data

In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C ^2m -boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L ^p -L ^q -regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on and the Lopatinskii–Shapiro condition on are necessary for these L ^p -L ^q -estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.      

Counting cycles and finite dimensional L norms

We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both ∑_i=1ⁿx_i^k and ∑_i=1ⁿ|x_i|^k, subject to the constraints that ∑_i=1ⁿx_i²=C and ∑_i=1ⁿx_i=0.     

Lp(Ω)空间上的Coherent风险度量

本文在Banach空间L^P(Ω)上定义Coherent风险度量ρ：L^P(Ω)→R，证明了ρ是下半连续的Coherent风险度量当且仅当存在Banach空间L^q(Ω)中的一个弱^*闭凸概率测度集Q使得ρ(X)=Z∈Q^sup E(-X/rZ)，其中1/p 1/q=1,推广了[3]中的部分结果。     

Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables

The properties of L₂-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L₂-approximable sequences since 1976 when Moussatat introduced a narrower notion of L₂-generated sequences. The method relies on a study of certain linear operators in the spaces L_p and l_p. A criterion of L_p-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.     

Sub-Laplacians of Holomorphic L-type on Rank One AN-Groups and Related Solvable Groups

Consider a right-invariant sub-Laplacian L on an exponential solvable Lie group G, endowed with a left-invariant Haar measure. Depending on the structure of G and possibly also that of L, L may admit differentiable L^p-functional calculi, or may be of holomorphic L^p-type for a given p≠2, as recent studies of specific classes of groups G and sub-Laplacians L have revealed. By “holomorphic L^p-type” we mean that every L^p-spectral multiplier for L is necessarily holomorphic in a complex neighborhood of some point in the L²-spectrum of L. This can only arise if the group algebra L¹(G) is non-symmetric. In this article we prove that, for large classes of exponential groups, including all rank one AN-groups, a certain Lie algebraic condition, which characterizes the non-symmetry of L¹(G) [37], also suffices for L to be of holomorphic L¹-type. Moreover, if this condition, which was first introduced by J. Boidol [6] in a different context, holds for generic points in the dual * of the Lie algebra of G, then L is of holomorphic L^p-type for every p≠2. Besides the non-symmetry of L¹(G), also the closedness of coadjoint orbits plays a crucial role. We also discuss an example of a higher rank AN-group. This example and our results in the rank one case suggest that sub-Laplacians on exponential Lie groups may be of holomorphic L¹-type if and only if there exists a closed coadjoint orbit Ω * such that the points of Ω satisfy Boidol's condition. In the course of the proof of our main results, whose principal strategy is similar as in [8], we develop various tools which may be of independent interest and largely apply to more general Lie groups. Some of them are certainly known as “folklore” results. For instance, we study subelliptic estimates on representation spaces, the relation between spectral multipliers and unitary representations, and develop some “holomorphic” and “continuous” perturbation theory for images of sub-Laplacians under “smoothly varying” families of irreducible unitary representations.     

不同风险度量约束下带有红利的投资组合模型研究

对现有的在风险度量约束下的投资组合模型进行了推广.建立了带有红利情形的随机股票市场模型,给出了投资组合关于这些风险度量约束下的最优化结果.     

直线上子集的H~s-拓扑及其应用

本文利用s-维Hausdorff测度给出了直线上一个子集E上的H~s拓扑和H~s-连通度的定义.讨论了它们的性质及其应用,解决了紧的s-集在欧氏拓扑下往往不连通的问题.     

Additive L-theory

The cobordism groups of quadratic Poincaré complexes in an additive category with involution are identified with the Wall L-groups of quadratic forms and formations in , generalizing earlier work for modules over a ring with involution by avoiding kernels and cokernels.