维林肯-傅里叶级数的（C，α）和

对维林金系统{ψ,n≥1}和0＜α＜ 1定义极大算子σ^α＊f：= sup │σ^αnf│，其中σ^αnf是函数f的（C，α）平均值．证明了算子σ^α＊是（p，p）型（1〈P〈∞）和弱（1，1）型．另外‖σ^α＊f‖1≤C‖f‖H1,，其中H1是Hardy空间．利用上述结果，证明了对任一可积函数f，σ^αnf几乎处处收敛于f．     

PrO-C*-代数的顺从性和核性

研究了Pro—C^*-代数的顺从性和核性．主要证明了(1)顺从Pro—C^*代数的闭理想是顺从的；(2)核Pro—C^*代数类对归纳极限封闭；(3)交换σ-C^*-代数和核C^*-代数都是核，σ-C^*-代数并且核σ-C^*-代数类对于商运算、张量积运算和可数逆向极限封闭．进一步得到核，σ-C^*-代数的扩张保持核性的条件。     

算子权移位的本质谱和Banach约化性

刻划了算子权移位S的本质谱σe(S)及其洞上的指标;讨论了S的Banach 约化性,并且刻划了S*成为Cowen-Douglas算子的条件.     

多复变数全纯映射精细的Bohr定理

本文首先建立不依赖自同构从复Banach空间平衡域到Cn单位多圆柱上一定限制条件下全纯映射精细的范数型Bohr定理及复Banach空间X上单位球到复Banach空间Y上单位球全纯映射精细的泛函型Bohr定理.其次,给出有界对称域上全纯映射精细的Bohr定理.最后,得到J*代数单位球上全纯映射精细的Bohr定理.所得结果将一维的Bohr定理推广至高维.     

A multidimensional central limit theorem with speed of convergence for axiom a diffeomorphisms

Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^fdm = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ²:=σ² （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ² . Moreover, there exists a real number A > 0 such that, for any integer n ≥ 1,Π( m*（ 1√ nS f n ）,N （0,σ² ） ≤A√n, where m*（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.     

复Banach空间中C-R方程的全纯解

二重复数是复数的一种推广，在其上的全纯映照族对应于Ｃ２上满足复Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯映照族．可以证明，这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族．本文证明：即使在Ｂａｎａｃｈ空间中，Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯解，具有同样的性质．     

Multiplicative Decompositions of Holomorphic Fredholm Functions and ψ*-Algebras

In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness of S(z) depends on the number of complex variables. The Multiplicative Decomposition theorem (0.1) sharpens the authors' Regularization theorem [11]; in case of the Band algebra L(X) of all bounded linear operators on a Band space, (0.1) has been proved by J. Letterer [20] for one complex variable and by M. 0. Zaidenberg, S. G. Krein, P. A. Kuchment and A. A. Pankov [26] for the Banach ideal of compact operators.     

Optimal Due-Date Determination and Sequencing of <Emphasis Type="Italic">n</Emphasis> Jobs on a Single Machine

Given a set of n jobs with deterministic processing times and the same ready times, the problem is to find the optimal processing-time multiple k* for the T.W.K. due-date assignment method, and the optimal sequence σ* to minimize the total amount of missed due-dates. It is found that k* is a constant for a given job set and σ* should be in S.P.T. sequence. After the theoretical treatment, a numerical example is given for discussion. The optimal results can readily be extended to situations in which the processing times are random variables with known means and having the same coefficient of variation. From a practical point of view, the main merit of this paper is that it demonstrates how, under certain production environments in which completion times of the jobs can be anticipated, to determine the optimal due-dates and obtain the optimal sequence.     

THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.     

Complex planar splines

In contradistinction to the known theory on complex splines which are defined on the boundary of a region in , we define complex planar splines on a region itself as a complex valued continuous function which is defined piecewise on suitable meshes of that region. The main idea is to use nonholomorphic functions as pieces, since holomorphic pieces would lead to just one holomorphic function on the whole region. Some of the techniques used are available from the theory of finite elements. But we also consider new aspects, namely, mapping properties of a complex planar spline v and the difference f − v, where f is, in general, a holomorphic function. For triangular meshes, rectangular and parallelogrammatic meshes, and meshes on circular sectors, explicit expressions are provided; also properties of the newly introduced complex planar splines are studied.     

Analytic discs under sympletic transforms

By a holomorphic homogeneous symplectic transformation of T*X (for X = ?^N), we interchange the conormal bundle T _M ^* X to a higher codimensional submanifold M with the conormal bundle T _M ^* X to a hypersurface M of X. For an analytic disc A “attached” to M we are able to find a section A* ?T*X with π A* = A, attached to T _M ^* X, such that Ã:= πx(A*) is an analytic disc “attached” to M. By this procedure of “transferring” analytic discs, we get the higher codimensional version of our criteria of [5] on holomorphic extension of CR functions (with [5] being on its hand the main tool of the present proof). Thus, let W be a wedge of X with generic edge M and assume that there exists an analytic disc contained in M ∪ W, tangent to M at a boundary point z₀∈ ?A, and not contained in M in any neighborhood of z₀. Then germs of holomorphic functions on W at z₀ extend to a full neighborhood of z₀.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

On Runge approximation in a Banach space

We show that on some open sets, more general than balls, Runge approximation is possible in certain Banach spaces, and also in certain complex Banach manifolds. We also show that there is an entire holomorphic curve in Hilbert space on which there is a bounded holomorphic function on the trace of a ball that has no bounded holomorphic extension to even a smaller concentric ball. Using the same technique we also prove that a form of Runge approximation better than an error function is not always possible.     

拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.     

Milnor numbers and Euler obstruction*

Using a geometric approach, we determine the relations between the local Euler obstruction Eu_f of a holomorphic function f and several generalizations of the Milnor number for functions on singular spaces. *This work was partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401.     

von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory

Recently, a class of Type II factors has been constructed, arising from holomorphic coverings of bounded planar domains. Those operators in Type II factors act on the Bergman space. In this paper, we develop new techniques to generalize those results to the case of the weighted Bergman spaces. In addition, a class of group-like von Neumann algebras are constructed, which are shown to be *-isomorphic to the group von Neumann algebras.     

复合形在欧氏空间中的实现问题Ⅲ

<正> 设 K 是一个有限单形复合形,我们恒可视 K 为一充分高维数 N 的欧氏空间中的欧氏复合形,此时其所定空间将记为(?).在研究 K 是否可实现于某一确定维数 m 的欧氏盘间R~m 中的时候,我们曾引进下面的一些定义(见[1],记号略有不同):     

Global Representatives of Colombeau Holomorphic Generalized Functions

It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on Ω, which is equal to zero in an open set L ì WL\subset{\rm{\Omega}} , is equal to zero.     

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmüller space AT(D) are studied in this paper. It is proved that if μ is asymptotically extremal in [[μ]] with h_ζ~*(μ) h~*(μ) for some point ζ∈ ?D, then there exist infinitely many geodesic segments joining [[0]]and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [[μ]] in AT(D).     

Loewner's theorem for kernels having a finite number of negative squares

By a theorem of Loewner, a continuously differentiable real-valued function on a real interval whose difference quotient is a nonnegative kernel is the restriction of a holomorphic function which has nonnegative imaginary part in the upper half-plane and is holomorphic across the interval. An analogous result is obtained when the difference-quotient kernel has a finite number of negative squares.