论奇单叶函数的Hayman猜测

设表示奇次近于凸函数全体。本文彻底解决C(S_2)族函数相邻两系数模模差的Hayman猜测,我们的结论是:||b_n|-|b_(n-1)||≤An~(-1/2)(n=2,3,…)其中A为绝对常数。     

Jackson算子关于二阶连续模的最佳逼近常数

求了用Jackson算子Jn（f.,x）逼近函数f（x）（∈C2n）时关于二阶连续模的最佳逼近常数：及用阶数不超过n的三角多项式H对连续函数f（x）的最佳逼近En（f）,的上界估计：     

算术级数中的奇数Goldbach问题

本文给出了算术级数的模的精确数值上界,在该算术级数中奇数Goldbach问题可解。我们的结果蕴含了Linnik常数的一个数值上界。     

论奇单叶函数的Hayman猜测

设f_2(z)=z sum from n=2 b_nz~(2n 1)∈C(S_2),C(S_2)表示奇次近于凸函数全体。本文彻底解决C(S_2)族函数相邻两系数模模差的Hayman猜测,我们的结论是:||b_n|-|b_(n-1)||≤An~(-(1/2))(n=2,3,…)其中A为绝对常数。     

Hadamard定理的积分形式

对闭圆环上的单值解析函数,当函数在两个边界圆上的最大模之比不是两个边界圆的半径之比的整数幂时,则Hadamard三圆定理中的严格不等式成立,即函数在环内的最大模有较小的上界.Teichmuller与Heins独立地得到了具有最大模的三圆定理的精确形式.本文用函数的积分平均模代替其最大模,同样得到了具有积分模的三圆定理的精确形式.     

抛物线模拔速度场的曲线积分问题

文章采用ｖｏｎＫａｒｍａｎ基本假设对模面函数为抛物线（又称喇叭模）的拔制问题设定了运动许可速度场，并经曲线积分与变上限积分得到拔制力的上界解析解。     

多元Stancu多项式与连续模

本文研究单纯形上多元Stancu多项式与连续模之间的关系,证明了Stancu多项式具有保持连续模的性质,推广了一元Bernstein多项式的相应结果.同时,利用多元函数的Ditzian-Totik连续模估计Stancu多项式逼近多元连续函数速度的上界和下界,得到一个使得逼近速度为O(n-a)(0相似文献   

关于Hayman问题与分担值

该文主要讨论Hayman的一个问题与分担值的联系，并运用新颖的方法证明了：设f 为非常数的整函数，n,k均为正整数，n≥k+1,a为非零的有穷复数，若a为f^n与(f^n)^(k)的分担值，则nf′=ωf，ω为方程t^k=1的根.     

幺模乘子在α模空间中的渐进估计

我们研究幺模乘子在α模空间中的渐进估计.对不同频率分解的空间进行统一的研究,包括模空间以及Besov空间.结果中的上界估计包含了已知的模空间的结果.同时,在对符号函数做局部非退化假设的条件下,给出幺模乘子的最佳渐进估计.     

幺模乘子在α模空间中的渐进估计北大核心CSCD

我们研究幺模乘子在α模空间中的渐进估计.对不同频率分解的空间进行统一的研究,包括模空间以及Besov空间.结果中的上界估计包含了已知的模空间的结果.同时,在对符号函数做局部非退化假设的条件下,给出幺模乘子的最佳渐进估计.     

Properties of boolean functions with a tree decomposition

Boolean functions that have a multiple disjoint decomposition scheme in the form of a tree are considered. Properties of such functions are given for the case that the functions are increasing, unate, and/or have no vacuous variables. The functions with a binary decomposition scheme are of special interest. The modulus of sensitivity is defined, and evaluated for some classes of functions. The modulus of sensitivity is interesting from the point of view of semantic information processing. It is found that the sensitivity for the class of functions with a given disjoint binary decomposition scheme is much smaller than for the unrestricted class of boolean functions. This indicates that these functions are potentially useful in pattern recognition of discrete data.The authors gratefully acknowledge the financial support of the National Research Council of Canada through a postdoctoral fellowship and an operating grant respectively.     

Некоторые точные нер авенства в теории при ближения функций

Exact inequalities are obtained that illuminate the interrelation between best polynomial approximations of functions, analytic in the disk and the modulus of continuity of the derivatives of the boundary values of these functions.For various classes of functions exact estimates are given for the derivative of a function by means of the modulus of continuity of this function and the modulus of continuity of its second derivative.As application, exact inequalities are deduced, analogous to the well-known Bernstein and Hardy inequalities.     

Exact estimates of regularity modulus for infinite programming

An exact estimate on the modulus of metric regularity for linear systems is given. By applying the estimate, we obtain explicit forms of the modulus for linear conical systems and differentiable nonlinear systems on the space of continuous functions.     

On some estimates for best approximations of bivariate functions by Fourier–Jacobi sums in the mean

Some problems in computational mathematics and mathematical physics lead to Fourier series expansions of functions (solutions) in terms of special functions, i.e., to approximate representations of functions (solutions) by partial sums of corresponding expansions. However, the errors of these approximations are rarely estimated or minimized in certain classes of functions. In this paper, the convergence rate (of best approximations) of a Fourier series in terms of Jacobi polynomials is estimated in classes of bivariate functions characterized by a generalized modulus of continuity. An approximation method based on “spherical” partial sums of series is substantiated, and the introduction of a corresponding class of functions is justified. A two-sided estimate of the Kolmogorov N-width for bivariate functions is given.     

Singular Integral Operators on Besov Spaces

Summary. We introduce generalized BESOV spaces in terms of mean oscillation and weight functions, following a recent work of Dorronsoro, and study the continuity of singular integral operators on them. Relations between these spaces and the BESOV spaces in terms of modulus of continuity are also studied. An application to pseudo-differential operators is given.     

Fourier coefficients of functions with a given modulus of continuity

In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.     

Strongly convex functions of higher order

The notion of strongly n-convex functions with modulus c>0 is introduced and investigated. Relationships between such functions and n-convex functions in the sense of Popoviciu as well as generalized convex functions in the sense of Beckenbach are given. Characterizations by derivatives are presented. Some results on strongly Jensen n-convex functions are also given.     

On Approximation for Certain Operators

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The Remainder Term for Analytic Functions of Symmetric Gaussian Quadratures

For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel . In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulus of the kernel on suitable ellipses is determined. Depending on the weight function the maximum modulus is attained at the intersection point of the ellipse with either the real or imaginary axis. Finally, a detailed discussion for some special weight functions is given.