共查询到20条相似文献,搜索用时 187 毫秒
1.
本文主要讨论Fréchet空间上ε-等距线性算子的等距逼近问题, 证明了任意有限维Fréchet空间之间的等距逼近问题都是肯定的; 无穷维Fréchet空间(s)空间上的等距逼近问题也是肯定的. 相似文献
2.
3.
本文在加权Lp范数逼近意义下确定了基于第一类Chebyshev 结点组的Lagrange 插值多项式列在一重积分Wiener 空间下同时逼近平均误差的渐近阶. 结果显示在Lp范数逼近意义下Lagrange 插值多项式列的平均误差弱等价于相应的最佳逼近多项式列的平均误差. 同时, 当2≤p≤4 时,Lagrange 插值多项式列导数逼近的平均误差弱等价于相应的导数最佳逼近多项式列的平均误差. 作为对比, 本文也确定了相应的Hermite-Fejér 插值多项式列在一重积分Wiener空间下逼近的平均误差的渐近阶. 相似文献
4.
首先给出赋范线性空间中的非空集合C的逼近紧性的等价描述. 如所周知, 如果C是Banach空间X中的一个逼近紧的半Chebyshev闭集, 那么由X到C的度量投影算子πc是连续的. 当X是中点局部一致凸的Banach 空间, 利用Banach空间几何的技巧证得: C的逼近紧性对投影算子πc的连续性也是必要的. 利用这个一般结论给出: 当T是由逼近紧且严格凸的Banach空间$X$到中点局部一致凸Banach空间Y的有界线性算子时, T有连续的Morse-Penrose度量广义逆T+$的充分必要条件. 相似文献
5.
本文讨论了Banach空间的一些逼近问题。给出了两个子空间的和可近的充要条件,对已知结果的推广,给出了连续函数空间和Lp(1≤p<∞)空间中的两个逼近定理。 相似文献
6.
研究一般Banach空间X 中同时逼近问题的适定性. 对严格凸的Kadec 空间X中的相对有界弱紧闭子集G,建立了关于最佳同时逼近问题适定Bair纲结果. 进一步, 当X是一致凸空间时, 证明了E(G)中使其最佳同时逼近问题不适定的序列在E(G)中是一个δ -多孔集. 另外, 还研究了关于最佳同时逼近元具有分歧域的集合G的几乎性. 相似文献
7.
在连续函数空间和L_p空间内研究算子逼近方法的基础上,利用一阶DitzianTotik积分模与不等式技巧研究了Bernstein-Durrmeyer-Bzier算子在Orlicz空间内的逼近性质.得到了Bernstein-Durrmeyer-Bezier算子在Orlicz空间内的逼近正定理和逼近等价定理.由于Orlicz空间比连续函数空间和L_p空间都"大",其拓扑结构也比L_p空间复杂得多,所以本文的结果具有一定的拓展意义. 相似文献
8.
本文研究了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近问题.借助了Jensen不等式,H?lder不等式,K泛函,光滑模等工具,获得了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近度,以及该算子的加权逼近,推广了lbragimov-Gadjiev-Durrmeyer算子在Lp空间中的逼近度及加权逼近. 相似文献
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论非周期函数在L~p空间中用奇异积分逼近 总被引:2,自引:0,他引:2
非周期函数在L~p空间中的逼近是逼近论中一个重要而又困难的问题.本文用新方法研究非周期函数在L~p空间中用奇异积分逼近,研究了逼近阶用连续模的估计问题,建立了一般定理,构造了一类对研究L~p空间中的逼近很有用的线性逼近方法,并给出了对多项式的应用. 相似文献
11.
Yu. A. Farkov 《Mathematical Notes》2000,68(2):248-254
Suppose thatB
R
d
is a ball of radiusR in ℂ
d
and σ is the standard measure on the unit sphere in ℂ
d
. ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH
R
0
(l, p, d) we denote the class of functionsf holomorphic inB
R
d
and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH
p
(B
R
d
). In this paper an asymptotic formula for the ε-entropy of the classH
R
0
(l, p, d) in the spacesL
p
(σ), 1≤p<∞, and
is obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000. 相似文献
12.
Andr Goldman Pierre Calka 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2003,39(6):90-1082
Denote by (t)=∑n1e−λnt, t>0, the spectral function related to the Dirichlet Laplacian for the typical cell
of a standard Poisson–Voronoi tessellation in
. We show that the expectation E(t), t>0, is a functional of the convex hull of a standard d-dimensional Brownian bridge. This enables us to study the asymptotic behaviour of E(t), when t→0+,+∞. In particular, we prove that the law of the first eigenvalue λ1 of
satisfies the asymptotic relation lnP{λ1t}−2dωdj(d−2)/2d·t−d/2 when t→0+, where ωd and j(d−2)/2 are respectively the Lebesgue measure of the unit ball in
and the first zero of the Bessel function J(d−2)/2. 相似文献
13.
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all
root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M
2)−χ(M
10/(1−χ(M
2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M
2)−χ(M
2)/(1−χ(M
2)). Also we construct, for each integer n≥3, an example of a map f: K
n
→N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. 相似文献
14.
Abstract Consider two independent random variables x and y with means and standard deviations μ x ,μ y ,σ x , and σ y , respectively. Let F x (t) = P[(x - μ, x )/σ x ≤ t] and F y (t) = P[(y - μ y )/σ y ≤ t]. In this article we address the problem of testing the null hypothesis H 0 : F x ≡ F y , against the alternative H 1 : F x ≡ F y . A graphical tool called T 3 plot for checking normality of independently and identically distributed univariate data was proposed in an earlier article by Ghosh. In the present article we develop a two-sample T 3 plot where the basic statistic is the normalized difference between the T 3 functions for the two samples. Significant departure of this difference function from the horizontal zero line is indicative of evidence against the null hypothesis. In contrast to the one-sample problem, the common distribution function under the null hypothesis is not specified in the two-sample case. Bootstrap is used to construct the acceptance region under H 0, for the two-sample T 3 plot. 相似文献
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Najla A. Altwaijry 《Journal of Functional Analysis》2008,254(11):2866-2892
The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy
0?D(u,u)+D(v,v)?idA, 相似文献
17.
We study the attractors of a finite system of planar contraction similarities S
j
(j=1,...,n) satisfying the coupling condition: for a set {x
0,...,x
n} of points and a binary vector (s
1,...,s
n
), called the signature, the mapping S
j
takes the pair {x
0,x
n} either into the pair {x
j-1,x
j
} (if s
j
=0) or into the pair {x
j
, x
j-1} (if s
j
=1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis. 相似文献
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Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
20.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献