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．     

非周期神经网络及平移网络在L_w~p中的逼近

设s≥d≥1为整数, 1≤p≤+∞,借助于正交多元代数多项式系而构造了一类s维网络算子,并用于逼近Lpw[-1,1]s中的函数,给出了逼近的上界以及当此算子为平移网络算子及神经网络算子时的导数型估计.     

赋Amemiya-Orlicz范数的Musielak-Orlicz-Sobolev空间单调性在最佳逼近中的应用

利用Musielak-Orlicz-Sobolev空间的构成特点,借鉴Orlicz-Sobolev空间的单调性在最佳逼近中的一些应用,以Orlicz空间中Jensen'S不等式的推广为主要工具,讨论了赋Amemiya-Orlicz范数的Musielak-Orlicz-Sobolev空间中的最佳逼近问题,主要是唯一性、存在性、稳定性.     

关于四元数矩阵的最佳逼近问题

通过使用四元数矩阵的广义奇异值分解,给出了四元数矩阵最佳逼近问题‖AHXA-C‖2F+‖BHXB-D‖2F=min, s.t. XH=X的一般表达式.     

Banach空间中太阳集对无穷序列的最佳同时逼近

本文研究太阳集对一列无穷序列的最佳同时逼近问题，建立了特征及唯一性结果．     

B_a空间中神经网络和平移网络的逼近

讨论了具一个隐层单元的神经网络在Ba空间中逼近的特征性定理并给出了逼近估计.对于平移网络,建立了Favard型估计.Orlicz空间中的相应结果均作为应用而给出.     

On the Best Approximation by Ridge Functions in the Uniform Norm

We consider the best approximation of some function classes by the manifold M _n consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W _p ^r,d from the manifold M _n in the space L _q for any 2≤ q≤ p≤∈fty behaves asymptotically as n ^-r/(d-1) . In particular, we obtain this asymptotic estimate for the uniform norm p=q=∈fty . January 10, 2000. Date revised: March 1, 2001. Date accepted: March 12, 2001.     

关于赋范线性空间中的三类泛函方程

在赋范线性空间中考察下列几类泛函方程( ) f(x) g(y) =h(x+y) ,　 ( ) f(x+y) =f(x) f(y) ,　 ( ) f(x+y) =f(x) +f(y) +ag(x) g(y)的性质与解以及彼此之间的关系 .     

赋Orlicz范数的Orlicz空间中最佳逼近算子

在赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间中,给出最佳逼近算子单调性的一个充分条件和最佳逼近元存在定理．     

On Copositive Approximation in Spaces of Continuous Functions Ⅱ:The Uniqueness of Best Copositive Approximation

This paper is part Ⅱ of "On Copositive Approximation in Spaces of Continuous Functions". In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Chebyshev subspace of C(Q), then for any admissible function f ∈C(Q)\M, the best copositive approximation to f from M is unique.     

Best Basis Selection for Approximation in L p

We study the approximation of a function class F in L _p by choosing first a basis B and then using n -term approximation with the elements of B . Into the competition for best bases we enter all greedy (i.e., democratic and unconditional [20]) bases for L _p . We show that if the function class F is well-oriented with respect to a particular basis B then, in a certain sense, this basis is the best choice for this type of approximation. Our results extend the recent results of Donoho [9] from L ₂ to L _p , p\neq 2 .     

On Copositive Approximation in Spaces of Continuous Functions I:The Alternation Property of Copositive Approximation

In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compact subset of real numbers. At the end of the paper the author applies this result for different classes of Q.     

On Measures Induced by Extremal Signatures in Best Real Polynomial Approximation

We consider the limit distribution of measures μ _n , that appear in extremal signatures in the best polynomial approximation of a real-valued function . Relations between structural properties of the function f and weak-star limit points of (μ _n ) _n are proved. April 4, 1996. Date revised: October 25, 1996.     

On Converse Theorem of Best Approximation by Polynomials in Bergman Spaces H_q~p(p>0,q>1)

A Bernstein type theorem and a converse theorem of best approximation by polynomials inBergman spaces H_q~p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.     

$L_{p}$空间修正插值多项式的逼近

本文考虑了函数f∈L_P[0,2π],1≤p<∞的特定的修正插值多项式,并给出了插值多项式对函数f的逼近速度的估计.本文的估计改进了Metelichenko最近的结果.     

Bergman空间B_q~p(p>0,q>1)中的多项式最佳逼近的逆定理

本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式逼近该空间函数的最佳逼近误差的阶的估计的逆定理．     

Bergman空间B_q~p(p>0,q>1)中的多项式最佳逼近的逆定理

本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式逼近该空间函数的最佳逼近误差的阶的估计的逆定理．     

一类修正的和与积分混合型算子的$L_p$逼近

The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.     

W_2~m[a,b]空间中线性泛函最佳逼近的深入讨论

本文基础上给出了Wm2(a,b)空间再生核构造的普遍方法,并利用再生核讨论算于插值样条的投影性质及最佳数值逼近问题