Cohen-Eisenstein级数与Shimura提升的一个推广

引进一类半整权模形式, 它们可以看做同余子群Γ₀(4N), 其中N是无平方因子的奇正整数上的Cohen-Eisenstein级数的一个自然推广. 应用这些级数, 证明了Shimura提升在Eisenstein空间E⁺_k+1/2(4N,x_l )上的限制, 给出一个从E⁺_k+1/2(4N,x_l )到E_2k(N)的同构.     

复指数Dirichlet 级数所表示的整函数的增长性

由Dirichlet 级数表示的整函数f(z)在带形中有界,其系数{a_n}和指数 {λ_n}(n=1,2,... )是复数列.文中引入 φ-级 和下φ -级,讨论f(z) 具有φ -级和下φ -级的条件.     

Hilbert变换相关的分布空间及其应用

本文构造了一个新的分布空间D′_H, 并且把经典的Hilbert变换的定义 推广到这个空间上. 证明了推广的Hilbert变换是把空间D′_H映射到自身的 同胚映射, 且D′_H是满足该条件的D′的最大子空间. 进一步, 证明了L^p空间中经典的Hilbert变换和周期函数空间中周期Hilbert变换都是这一推广Hilbert变换的特款. 对空间D_H的性质进行了刻画, 并给出了空间D′_H中的一类非常有用的非线性相位信号. 最后给出了该推广Hilbert变换的两个简单的应用.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

∑e1型Banach空间上C0半群稳定性的谱特征

讨论一类不可分解的∑_e¹型Banach空间上有界线性算子的谱的特殊性质;给出了∑_e¹型Banach空间上一致有界C₀半群稳定性的一个谱特征,并给出稳定性定理的一个应用.     

Banach空间的逼近紧性与度量投影算子的连续性及其应用

首先给出赋范线性空间中的非空集合C的逼近紧性的等价描述. 如所周知, 如果C是Banach空间X中的一个逼近紧的半Chebyshev闭集, 那么由X到C的度量投影算子π_c是连续的. 当X是中点局部一致凸的Banach 空间, 利用Banach空间几何的技巧证得: C的逼近紧性对投影算子π_c的连续性也是必要的. 利用这个一般结论给出: 当T是由逼近紧且严格凸的Banach空间$X$到中点局部一致凸Banach空间Y的有界线性算子时, T有连续的Morse-Penrose度量广义逆T⁺$的充分必要条件.     

单位球上μ-Block空间之间的加权复合算子

到了Cⁿ中单位球上加权复合算子T_ψ,φ为空间β_μ到β_υ以及空间β_μ,0到β_υ,0之 有界算子和紧算子的充要条件, 同时也得到了一系列相关推论.     

Al-Mg2Si共晶合金在“神舟2号”飞船上定向复合生长

在我国“神舟2号”飞船上进行的Al-Mg₂Si共晶合金的定向生长样品的初步分析结果. 分析表明微重力对Al-Mg₂Si共晶合金的定向生长有影响. 空间凝固样品中的共晶团比地面的粗大, 定向生长效果比地面样品的差, 但片层厚度没有显示出明显差异, 而空间样品中平均片层间距比地面样品中的小. 并就空间环境对Al-Mg₂Si共晶合金的定向生长的影响进行了讨论.     

弱Hardy鞅空间与鞅的弱原子分解

定义了一些弱Hardy鞅空间和3种类型的弱原子. 它们与经典的H_p鞅论中的Hardy鞅空间和原子形成对应. 然后证明了弱Hardy鞅空间上的3个弱原子分解定理. 利用鞅的弱原子分解, 给出了弱Hardy鞅空间上的次线性算子有界的一个充分条件. 利用这个条件, 得到关于鞅的一系列弱H_p范数不等式和弱(p,p)型不等式, 以及各个弱Hardy鞅空间的连续嵌入关系. 这些不等式是经典的H_p鞅论中基本不等式的弱型对应.     

Bergman空间上的区域积分算子

刻画单位圆盘D上的非负测度μ, 它使得 从 Bergman 空间A^α_p到 空间 L^q(∂D)$的区域积分算子A_μ 有界.     

一类不可分的 Bα函数空间

Ba 函数空间是由丁夏畦教授和罗佩珠教授在文[1—3]中引入的.它已得到了大量应用(参见[4—8]).由于 Ba 函数空间是由一列 L_p 空间产生的(定义见第二节),人们自然会提出如下问题:问题 A.若已知某性质对 L_p 空间成立,是否可得出该性质对 Ba 函数空间也成立     

COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

Answering an old problem in nonlinear theory, we show that c₀cannot be coarsely or uniformly embedded into a reflexive Banachspace, but that any stable metric space can be coarsely anduniformly embedded into a reflexive space. We also show thatcertain quasi-reflexive spaces (such as the James space) alsocannot be coarsely embedded into a reflexive space and thatthe unit ball of these spaces cannot be uniformly embedded intoa reflexive space. We give a necessary condition for a metricspace to be coarsely or uniformly embeddable in a uniformlyconvex space.     

加权复合算子在Bloch型空间上的有界性

In this paper,we give a necessary and sufficient condition for weighted composition operators Cu,ψ to be boundedness on Bloch type spaces Ba.The theorem generalizes some previous results.     

On Weighted Spaces of Harmonic and Holomorphic Functions

Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c₀. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c₀. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded.     

Walls for Gieseker semistability and the Mumford-Thaddeus principle for moduli spaces of sheaves over higher dimensional bases

Let X be a projective manifold over \Bbb C \Bbb C . Fix two ample line bundles H₀ and H₁ on X. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lying in the cone spanned by H₀ and H₁. We attempt a new definition of walls which naturally describes the behaviour of Gieseker semistability. By means of an example, we establish the possibility of non-rational walls which is a substantially new phenomenon compared to the surface case. Using the approach by Ellingsrud and Göttsche via parabolic sheaves, we were able to show that the moduli spaces undergo a sequence of GIT flips while passing a rational wall. We hope that our results will be helpful in the study of the birational geometry of moduli spaces over higher dimensional bases.     

Some New Relations Between Stokes's Coefficients in the Theory of Gravity Waves

Stokes's method of calculating the form of steady finite-amplitude,gravity waves in deep water involves a series of coefficientsC_n related to the Fourier coefficients of the free surface elevation.The condition of constant pressure at the free surface yieldsa series of cubic relations between the C_n, which are normallyused for calculations. In this paper it is shown that the C_nalso satisfy some simpler, quadratic relations, which renderthe calculation of the profile faster and more accurate. The new relations are equivalent to certain integral propertiesinvolving the square of the particle speed, integrated alonga streamline. This enables a generalization to be readily madeto waves in water of finite depth.     

Strong Weighted Mean Summability and Kuttner's Theorem

In this paper we study sequence spaces that arise from the conceptof strong weighted mean summability. Let q = (q_n) be a sequenceof positive terms and set Q_n = ⁿ_k=1q_k. Then the weighted meanmatrix M_q = (a_nk) is defined by if kn, a_nk=0 if k>n. It is well known that M_q defines a regular summability methodif and only if Q_n. Passing to strong summability, we let 0<p<.Then , are the spaces of all sequences that are strongly M_q-summablewith index p to 0, strongly M_q-summable with index p and stronglyM_q-bounded with index p, respectively. The most important specialcase is obtained by taking M_q = C₁, the Cesàro matrix,which leads to the familiar sequence spaces w₀(p), w(p) and w(p), respectively, see [4, 21]. We remark that strong summabilitywas first studied by Hardy and Littlewood [8] in 1913 when theyapplied strong Cesàro summability of index 1 and 2 toFourier series; orthogonal series have remained the main areaof application for strong summability. See [32, 6] for furtherreferences. When we abstract from the needs of summability theory certainfeatures of the above sequence spaces become irrelevant; forinstance, the q_k simply constitute a diagonal transform. Hence,from a sequence space theoretic point of view we are led tostudy the spaces     

The Generation of Chisholm Rational Polynomial Approximants to Power Series in Two Variables

The generation of successive Chisholm rational polynomial approximantsf_m/_m of f(x, y), a power series in two variables, is discussed. A necessary and sufficient condition for the non-degeneracyof f_m/_m is given. It is shown that the non-degeneracy of thediagonal Pad? approximants of order m in each variable separatelyis a necessary condition for the non-degeneracy of f_m/_m. In the case of a symmetric function, it is proved that the Chisholmapproximant f_m/_m is symmetric and non-degenerate if and onlyif all the diagonal Pad? approximants of order up to m in onevariable are non-degenerate. The generation of successive Chisholmapproximants to symmetric functions is also considered. The computational scheme, called the prong method, extends tocover the computation of Chisholm approximants in N-variables(Chisholm & McEwan, 1974).     

Symmetric Polynomials on Rearrangement-Invariant Function Spaces

The exact representation of symmetric polynomials on Banachspaces with symmetric basis and also on separable rearrangement-invariantfunction spaces over [0, 1] and [0, ) is given. As a consequenceof this representation it is obtained that, among these spaces,l_2n, L_2n[0, 1], L_2n[0, ) and L_2n[0, )L_2m[0, ) where n, m areboth integers are the only spaces that admit separating polynomials.