复赋范空间中的同时太阳集的最佳逼近

研究了复赋范空间中的同时太阳集对无穷序列的最佳逼近问题，得到了特征及唯一性定理．     

复Grassmann流形中的全纯2-球面

研究复Grassmann流形G(k ,n)中的全纯 2 球面S² ,导出了广义Frenet公式和广义Plücker公式.利用这些公式得到一些曲率pinching定理.还给出了G(k ,n)中Einstein全纯S² 的结构定理.     

复正规多项式系统的全局通解

本文首先应用复多项式系统的强有根定理,证明了一类复多项式系统全局通解的存在性.其次,讨论了正规多项式系统全局通解的定性结构,得到了它的表示定理.最后给出了定理应用的例子.     

复k-超正则函数和复k-超调和函数

首先利用Stokes-Green定理得到了复k-超正则函数的必要条件.其次得到了复k-超正则函数和复k-超调和函数的充要条件.最后讨论了复k-超正则函数和复k-超调和函数的关系:已知一个复k-超调和函数u(z),局部存在复k-超正则函数f(z)使得Pf(z)=u(z)等.     

复罗尔定理

复罗尔定理俞飞，余继光，史元祜（淮南联合大学）一、引言众所周知，许多古典的实分析结论是罗尔定理和中值定理的推论。一般情况下，由巴拿赫空间的子集映射到另一子集时，中值定理是一个适合于许多应用的不等式，但不适合于建立如同实变量的罗尔定理的等式。最近，有关...     

复高阶差分方程解

利用亚纯函数的Nevanlinna值分布理论,讨论了两类复高阶差分方程亚纯解的存在性和增长级问题,一类复差分方程的Malmquist型定理被建立,另一类复差分方程解的增长级得到估计.例子表明了我们的结果是精确的.     

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.     

模糊复测度空间上可测函数列几种收敛性之间的关系

作为经典复测度和模糊测度的推广,研究模糊复测度及模糊复测度空间上可测函数列几种收敛性之间的关系.在模糊复测度空间上得到了Egoroff定理、Lebesgue定理和Riesz定理等重要结果.为模糊复分析的深入研究打下一定基础.     

关于两类复微分方程组的允许解

本文利用Nevanlinna值分布理论讨论了复平面内两类复微分方程组的允许解的存在性问题,改进了文[1]中的一些定理,从而得到了更精确、更一般的结果     

Malmquist型复差分方程组

近来一些论文里,Ablowitz,Halburd以及Herbst等人应用Nevanlinna理论证明了类似于复微分方程Malmquist定理的复差分方程一些结果.本文主要研究一类复差分方程组的Malmquist定理,推广和改进了他们的一些结论.     

Characterization of best uniform approximation with restricted ranges of derivatives

This paper gives a general characterization theorem of a best uniform approximation of generalized polynomial having multiple restricted ranges of its derivatives. This theorem is widely applicable. The results on characterization in many standard approximations, such as approximation with Hermite-Birkhoff interpolatory side conditions, multiple comonotone approximation, and approximation by algebraic polynomials having bounded coefficients, etc., are special cases of our results.     

On the best approximation of vector valued functions by polynomials with coefficients in vector spaces

In this paper, we prove some basic results concerning the best approximation of vector-valued functions by algebraic and trigonometric polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain direct and inverse theorems for the best approximation by generalized polynomials and results concerning the existence (and uniqueness) of best approximation generalized polynomials. This paper was written during the 2005 Spring Semester when the second author (S.G. Gal) was a Visiting Professor at the Department of Mathematical Sciences, The University of Memphis, TN, USA. Mathematics Subject Classification (2000) 41A65, 41A17, 41A27     

A new generalization of complex Stancu operators

In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk.     

Haar锥逼近的交错定理及其在系数有界逼近中的应用

本文首先推广了Ｐ．Ｐｅｉｓｋｅｒ １９８３年给出的Ｈａａｒ锥的定义及Ｈａａｒ锥一致逼近的交错定量，然后得到了Ｈａａｒ锥根数的一种求法。利用这些结果，讨论了系数有界限逼近的特征问题，特别是给出了系数有界限的代数多项式逼近与广义Ｂｅｒｎｓｔｅｉｎ多项式逼近的使用十分方便的交错定理。     

General characterization of best approximation and its application to uniform approximation with restricted ranges

Let R be a normed linear space, K be an arbitrary convex subset of an n-dimensional subspace Φ _n ⊂R. This paper first gives a general charactaerization for a best approximation from K in form of “zero in the convex hull”. Applying it to the uniform approximation by generalized polynomials with restricted ranges, we get further an alternation characterization. Our results ocntains the special cases of interpolatory approximation, positive approximation, copositive approximation, and the classical characterizations in forms of convex hull and alternation in approximation without restriction.     

Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials

Summary. The paper presents results on the approximation of functions which solve an elliptic differential equation by operator adapted systems of functions. Compared with standard polynomials, these operator adapted systems have superior local approximation properties. First, the case of Laplace's equation and harmonic polynomials as operator adapted functions is analyzed and rates of convergence in a Sobolev space setting are given for the approximation with harmonic polynomials. Special attention is paid to the approximation of singular functions that arise typically in corners. These results for harmonic polynomials are extended to general elliptic equations with analytic coefficients by means of the theory of Bergman and Vekua; the approximation results for Laplace's equation hold true verbatim, if harmonic polynomials are replaced with generalized harmonic polynomials. The Partition of Unity Method is used in a numerical example to construct an operator adapted spectral method for Laplace's equation that is based on approximating with harmonic polynomials locally. Received May 26, 1997 / Revised version received September 21, 1998 / Published online September 7, 1999     

Approximation by complex genuine Durrmeyer type polynomials in compact disks

In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex genuine Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for the genuine Durrmeyer polynomials, namely the extensions of the approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane.     

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω ² u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.     

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω ² u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.