Interpolation Operators on the Space of Holomorphic Functions on the Unit Circle

The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval [—a, a],a (0,1), have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general extremal problem with free weights and knots is solved.     

A Non-Uniform Estimate in the Central Limit Theorem for Sequences of Strongly Additive Functions

The value distribution of a normalised sequence of strongly additive arithmetic functions

一类指数型整函数插值算子的逼近性质(2)

本文研究了一类指数型整函数插值算子在C（R）和Lp(1≤p≤∞）空间上的饱和性质。     

The Approximation Properties of Certain Interpolation Operators of Entire Exponential Type（1）

In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)     

Convergence of Lagrange Interpolation Polynomials for Piecewise Smooth Functions

The present paper first establishes a decomposition result for f(x)∈ C ^r C ^r+1. By using this decomposition we thus can obtain an estimate of ∣f(x) - L _n (f,x)∣ which reflects the influence of the position of the x's and ω(f ^(r+1),δ)_j, j = 0,1,...,s, on the error of approximation. This revised version was published online in June 2006 with corrections to the Cover Date.     

伪二元函数的Hermite插值

将一元函数的Hermite插值方法与伪二元函数结合,得到了伪二元函数的Hermite插值函数,并对插值函数进行了误差分析,最后给出了一个实例.     

非有限带函数由Hermite型多元样本定理的重构

In this paper, we prove that under some restricted conditions, the non-bandiimited functions can be reconstructed by the multidimensional sampling theorem of Hermite type in the space of Lp（R^n）, 1 〈 p 〈 ∞.     

振荡函数的Hermite数值积分公式

本文讨论了振荡函数形如∫１－１ｆ（ｘ）ｓｉｎωｘｄｘ，∫１－１ｆ（ｘ）ｃｏｓωｘｄｘ的Ｈｅｒｍｉｔｅ积分公式，它基于ｆ（ｘ）的Ｈｅｒｍｉｔｅ插值多项式的一些结论，导出了依赖于ｘｎｊ的ａｎｊ及不依赖于ｘｎｊ的ｇ（ｋ，ｗ）的权数因子的递推关系式，并给出误差分析．     

Interpolation Formula for Functions of Several Variables

Mathematical Notes -     

A Complement to the Valiron-Titchmarsh Theorem for Subharmonic Functions

The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n ≥ 3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0 ρ 1, then the existence of the limit limr →∞ logu(r)/N(r),where N(r) is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.     

用指数型整函数的最佳限制逼近

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.     

Lp空间有理插值型算子的逼近

考虑了两类有理插值型算子的Jackson型估计．当p〉1时．建立了Dilzian—Totik型定理，当p=1时．利用通常连续模给出了Jackson型估计．     

给定零点的指数型整函数Ⅱ

研究了如下问题:给定右半平面一复数列,以该复数列为零点的指数型整函数在虚轴上的增长性有什么表现?并给出了完整的解答.这是对Malliavin和Rubel关于给定右半平面一复数列为零点的指数型整函数性质的研究工作的一个推广.     

给定极点的有理函数插值序列的收敛性

设Γ∈Ｃ（１，α），α＞０．Ｇ是复平面上以Γ为边界的有界单连通区域．本文考虑了极点位于G外部，以广义Ｆａｂｅｒ-Ｄzｒｂａsｊａｎ有理函数的零点为插值结点的Ｌａｇｒａｎｇｅ插值有理函数序列对Ａ（G）和Ｅ^ｑ（Ｇ）（１＜ｑ＜＋∞）中函数的一致逼近和平均逼近阶的估计．     

一个无限可微函数类的最优Lagrange 插值

本文研究\,$[-1,1]$上的一个无限可微函数类$F_\infty$在空间$L_\infty[-1,1]$及加权空间$L_{p,\omega}[-1,1]$, $1\le p< \infty$ ($\omega$是$(-1,1)$上的非负连续可积函数)的最优Lagrange插值.我们证明了基于首项系数为1且于$L_{p,\omega}[-1,1]$上有最小范数的多项式零点的Lagrange插值对$1\le p< \infty$是最优的. 同时我们给出了当结点组包含端点时的最优结点组.     

The Levin-Golovin theorem for sobolev spaces

We obtain sufficient conditions for the basis property of the family of exponentials

An extremal problem for even positive definite entire functions of exponential type

We consider an extremal problem for even positive definite entire functions of exponential type with zero mean with power weight on the semiaxis. This problem is related to the multidimensional Jackson-Stechkin theorem in the space L ₂(?ⁿ).     

二元分形插值的拟合误差估计

A given bivariate continuous function is fitted by using a bivariate fractal interpolation function, and the error of fitting is studied in this paper. The results of error estimates are obtained in two metric cases. This provides a theoretical basis for the algorithms of fractal surface reconstruction.     

Formulas for Liapunov Functions for Systems of Linear Difference Equations

Explicit quadratic Liapunov functions that provide necessaryand sufficient conditions for the asymptotic stability of thesystem of linear difference equations x (t + 1) = Ax(t) areconstructed by transforming the original systems to y (t + 1)= Gy(t), where G is a companion matrix associated with the characteristicpolynomial of A. A necessary and sufficient condition for allroots of the characteristic polynomial to lie in the unit circle|z| < 1 on the complex plane is also derived. 2000 MathematicalsSubject Classification 39A11, 93D05.