THE GEL'FAND n-WIDTHS OF MULTIVARIATE PERIODIC BESOV CLASSES

The Gel'fand n-widths of Besov classes are considered. The weak asymptotic behavior is established for the corresponding quantity.

THE N-WIDTHS FOR A GENERALIZED PERIODIC BESOV CLASSES

In this paper, an extension of Besov classes of periodic functions on Td is given. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, and the Gel＇fand n-widths are obtained, respectively.

OPTIMAL ALGORITHMS FOR DIAGONAL OPERATORS ON N-WIDTHS IN DIFFERENT COMPUTATIONAL SETTING——In Memory of Professor Sun Yongsheng

In this paper, we give some optimal algorithms for diagonal operator T from space lp（1≤p≤2） to l2 on n-widths in different computational setting.

ESTIMATES OF LINEAR RELATIVE n-WIDTHS IN L^p [0,1]

In this paper we will show that if an approximation process {Ln}n∈N is shape- preserving relative to the cone of all k-times differentiable functions with non-negative k-th derivative on [0,1], and the operators Ln are assumed to be of finite rank n, then the order of convergence of D^kLnf to D^kf cannot be better than n-2 even for the functions x^k, x^k＋1, x^k＋2 on any subset of [0,1 ] with positive measure. Taking into account this fact, we will be able to find some asymptotic estimates of linear relative n-width of sets of differentiable functions in the space LP[0, 1], p ∈ N.

THI GENERALIZED RAYLEIGH SPECTRA AND KOLMOGOROV n-WIDTHS

Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of the approximation theory.We find the lower bound for Kolmogorov n-width d_n(F(Bl_p^m),l_q^m).

利用Gel'fand基计算SU(3)Clebsch-Gordan系数的Mathematica软件

利用Ｇｅｌ’ｆａｎｄ基和对相因子约定的分析，编写了一个计算ＳＵ（３）ＣｌｅｂｓｃｈＧｏｒｄａｎ（ＣＧ）系数的Ｍａｔｈｅｍａｔｉｃａ软件。其计算结果与广义ＣｏｎｄｏｎＳｈｏｒｔｌｅｙ相因子约定下的结果一致。

可剖分函数与Weak~*(S)积分(英文)

引进了 weak*(S) -积分的概念 ,并研究了积分 weak*(S) -与 Gel’fand积分之间的关系 .主要结果是 :当 X**是赋予 weak*拓扑的局部凸向量空间时 ,Weak*(S) -积分与

多元周期Sobolev类的Gel’fand宽度与Bernstein宽度

讨论多元周期Sobolev类Wrp(Td)及Wrp(M,Td)于Lq(Td)下的Gel fand n——宽度(1≤q≤p≤∞)及Bernstein n——宽度(1≤q≤p≤2),得到了相应量的弱渐近估计。

Gel＇fand三元组上由同一Lévy过程定义的不同分数Lévy过程之间的积分变换公式(英文)

本文利用Riemann-Liouville分数积分算子的半群性质以及分数Lévy过程的Wie-ner积分,给出由同一平方可积Lévy过程定义的不同分数Lévy过程之间的积分变换公式.

关于B-值广义白噪声泛函的VOLTERRA型积分方程

讨论了关于Banach值广义白噪声泛函的量子Volterra型积分方程,其中核为时空白噪声,自由项为取值于B值广义泛函空间的抽象函数.在此基础上,证明了:方程解的存在性,唯一性和强连续性.

关于纯N-孤立子解的新证明

本文对于Korteweg-de Vries方程的纯N-孤立子解,得出了新的证明。并由此推导出:t→±∞时,确实存在N个孤立波。且在t增加的过程中,不同的波经碰撞而不改变其形状。

Bernstein n-Widths for Classes of Convolution Functions with Kernels Satisfying Certain Oscillation Properties

In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.

On n-Widths of a Sobolev Function Class in Orlicz Spaces

This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov＇s widths, Gelfand＇s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.

On the 2n-Widths of a Periodic Sobolev Class

1 Introduction Let Q（x）be a polynomial with real coefficients and the Sobolev class Wp（Q（D））be the set of continuous 2π-periodic functions f（x） for which f（degQ-1） is absolutely continuous and ‖Q（D）f‖p≤1, where degQ is the degree of Q, D=d/dt, and ‖·‖p is the usual Lp[0, 2π]-

Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel

In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.

n-WIDTHS OF SOME CLASSES OF PERIODIC FUNCTIONS

Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspaces for d_(2n) and d^(2n) respectively, and construct an optimallinear operator of rank 2n for δ_(2n), from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W_(2n)={a +sum from i=0 to (2n-1) a_iG(x-iπ/n)a,a_i∈R,sum from i=0 to(2n-1) a_i=0} is an optimal subspace ford_(2n)(?_p,L_p) for p=q.

AVERAGE n-WIDTH OF POINT SET IN HILBERT SPACE

Given a separable real Banach space F and a separable real Hilbert space X, we denote by S a bounded linear operator from F into X. Let μ be a Gaussian measure defined on the Borel field of F with mean element m_μ= 0 and correlation operator C_μ. By [1], C_μ is a bounded linear operator from F~*→F such

Average optimization of the approximate solution of operator equations and its application

In this paper, a definition of the optimization of operator equations in the average case setting is given. And the general result (Theorem 1) about the relevant optimization problem is obtained. This result is applied to the optimization of approximate solution of some classes of integral equations.