共查询到20条相似文献,搜索用时 203 毫秒
1.
It is shown that a function f which is in the classical Paley-Wiener class, and its k-th derivative f(k) can be recovered in the metric Lq(R),2 < q ≤ ∞, from its values on irregularly distributed discrete sampling set {tj}j∈z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj}j∈z is a real sequence such that {eifj(?)}j∈z constitutes a Riesz basis for L2([-π,π]). 相似文献
2.
§ 1 IntroductionLet N be the set of all natural numbers.Write Z+=N∪ { 0 } ,Nn={ 1 ,2 ,...,n} andZn={ 0 }∪Nnfor any n∈N.Let X be a topological space and f:X→X be a continuous map.Forx∈X,O(x,f) ={ fk(x) :k∈ Z+} is called the orbit of x.The set of periodic points,the set of recurrentpoints,the set ofω-limit points for some x∈X and the set of non-wandering points of fare denoted by P(f) ,R(f) ,ω(x,f) andΩ(f) ,respectively(for the definitions see[1 ] ) .Let A X,we use int(A) ,A… 相似文献
3.
ON CONVERGENCE OF PAL-TYPE INTERPOLATION POLYNOMIALS 总被引:2,自引:0,他引:2
Xie Tingfan 《数学年刊B辑(英文版)》1988,9(3):315-321
Let {x_k~*}_(k=1)~(n-1) be the zeros of the (n-1) -th Legendre polynomial p_(n-1)(x) and {x_k}_(a=1)~n be the zeros of the polynomial w(x)= (1-x2~)p_(n-1)~1(x). By the theory of the Pal interpolation, for afunction f ∈ C_([-1,1])~1, there exists a unique polynomial Q_n(f, x) of degree 2n-1 satisfying conditions Q_n(f, x_k)=f(x_k), Q'_n(f, x_k~*)=f'(x_k~*), where k=1, 2, …, n and x_n~*=-1. The main result of this paper is that if f ∈ C_([-1,1])~r, thenf(x)-Q_n(f, x)=O(1)W(x)w(f~(r), 1/n)n~((1/2)-r), -1≤x≤1.Hence, if f ∈ C_[-1,1])~1, then Q_n(f, x) converges to the function f(x)uniformly on the interval [-1, 1]. 相似文献
4.
许宝刚 《数学物理学报(B辑英文版)》2004,24(4):603-607
Let I with |I| = k be a matching of a graph G (briefly, I is called a k-matching). If I is not a proper subset of any other matching of G, then I is a maximal k-matching and m(gk, G) is used to denote the number of maximal k-matchings of G. Let gk be a k-matching of G, if there exists a subset {e1, e2,…, ei} of E(G) \ gk, i (?)1, such that (1) for any j ∈ {1, 2,…,i}, gk + {ej} is a (k + l)-matching of G; (2) for any f ∈ E(G) \ (gk ∪ {e1,e2,…,ei}), gk + {f} is not a matching of G; then gk, is called an i wings k-matching of G and mi(gk,G) is used to denote the number of i wings k-matchings of G. In this paper, it is proved that both mi(gk,G) and m(gk,G) are edge reconstructible for every connected graph G, and as a corollary, it is shown that the matching polynomial is edge reconstructible. 相似文献
5.
Let D be the unit disc and H(D) be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H(D) : f(z) =sum from k=o to ∞ ak(z + 1)k, z∈ D, ‖f‖2 = sum from k=o to ∞ |ak|24k < ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied. 相似文献
6.
Let G(V, E) be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if (1) C(u)≠C(v) for uv ∈ E(G), where C(u) = {f(uv)|uv ∈ E}, and (2) for any i, j = 1, 2,… k, we have ||Ei| |Ej|| ≤ 1, where Ei = {e|e ∈ E(G) and f(e) = i}. χáve (G) = min{k| there exists a k-AVEEC of G} is called the adjacent vertex-distinguishing equitable edge chromatic number of G. In this paper, we obtain the χáve (G) of some special graphs and present a conjecture. 相似文献
7.
PARAMETER ESTIMATION OF SPATIAL AR MODEL 总被引:1,自引:0,他引:1
Jiang Jiming 《数学年刊B辑(英文版)》1991,12(4):432-444
Consider a stable AR model of two parameter spatial series {X_t, t∈N~2}, i. e. {X_(t)t∈N~2} is homogeneous and satisfies the following difference equationX_t-sum from n=s∈相似文献
8.
Chen Xiru 《数学年刊B辑(英文版)》1984,5(2):185-192
Let X_1,…,X_n be iid samples drawn from an m-dimensional population with a probabilitydensity f,belonging to the family C_(ka),i.e.the family of all densities whose partialderivatives of order k are bounded by a.It is desired to estimate the value of f at somepredetermined point a,for example a=0.Farrell obtained some results concerning the bestpossible convergence rates for all estimator sequence,from which it follows,for example,thatthere exists no estimator sequence{γ_n(0)=γ_n(X_1,…,X_n,0)}such that(?)E_f[γ_n(0)-f(0)]~2=o(n~(-2k/(2k m))).This article pursues this problem further and proves that there existsno estimator sequence{γ_n(0)}such thatn~(-k/(2k m))(γ_n(0)-f(0))(?)0,for each f∈C_(ka),where(?)denotes convergence in probability. 相似文献
9.
Let X be a Banach space with a weakly continuous duality map Jφ,C a non-empty weakly compact convex subset of X, and T:(T(t):t∈S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K∩F(T)≠0 is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit {u(t):t∈S} of T converges weakly to a point in F(T) if and only if {u(t):t∈S}is weakly asymptotically regular. 相似文献
10.
Shi Xianliang 《数学年刊B辑(英文版)》1982,3(3):365-374
The ( f,d_n) -summability method is defined as follows^[1,4]: Let f be a nonconstant
function, analytic in |z | < R for R > l, and let {d_n} be a sequence of complex numbers,such that for all n,$d_n \ne -f(1)$.Suppose that the elements of the metrix A = (a_nk) are given by the relations
$a_00=1,a_0k=0(k \geq 1)$
$[\prod\limits_{j = 1}^n {\frac{{f(z) + {d_j}}}{{f(1) + {d_j}}} = \sum\limits_{k = 0}^\infty {{a_{nk}}{z^k}} } \]$
A sequence {S_n} is said to be ( f, d_n), —summable to s, if \sigma_n = \sum\limits_{k=0}^\infty \arrow s as n \arrow \infty. The
( f, d_n) —summability method is said to be non-negative if for all n, d_n> 0 and the
Maclaurin coefficients of f are real and non-negative. The Lebesgue constants for the
( f,d_n)-method are defined by
$L_n(A)=2/\pi \int_0^\pi /2 {\frac{|\sum\limits_{k=0}^\infty {a_nk sin(2k+1)t|}{sint}dt}$
In this parer we prove the following two theorems. 相似文献
11.
涉及微分多项式的正规定则(英文) 总被引:1,自引:0,他引:1
本文获得如下结果:设φ(z)为区域G内一不恒为零的亚纯函数,a1(z),a2(z),.…,ak(z)为区域G内的全纯函数,F={f}为G内一亚纯函数族,若对每一f∈F,在G内恒有f(z),f(z)≠0,f^(k)(z) a1(z)f^(f-1)(z) … ak(z)f(z)≠φ(z),且与φ(z)没有公共极点,则F在G内正规。 相似文献
12.
Let Fκ = {χ ε (0,1)|{2^nχ} ≥ 1/2^κ,n ε Z }, Z = {0,1,2,3}, κ ε N;F = Uκ^∞=1Fκ be a decimal set in (0, 1), where {2^nχ} is the fractional part of a number 2^nχ. In this note, we prove that dimHF = 1 and H^1(F) =0, where dimH is Hausdr off dimension, and H^1(F) is the Hausdorff measure of F. 相似文献
13.
BU Shangquan 《数学年刊B辑(英文版)》2001,22(4):513-518
Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W… 相似文献
14.
15.
关于域上矩阵广义逆的加法映射 总被引:3,自引:0,他引:3
假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义. 相似文献
16.
亚纯函数的不动点与拟正规族 总被引:4,自引:0,他引:4
本文研究了亚纯函数的不动点与拟正规族的关系,得到了以下结果:设F 是区域D内的亚纯函数族,q是一个非负整数.如果对任意的f∈F存在自然数k=k(f)>1使得f的 k次迭代f~k在 D内最多有 q个不动点,则F是 D内阶至多为max{4,q+3}的拟正规族. 相似文献
17.
对简单图G(V,E),f是从V(G)∪E(G)到{1,2,…,k}的映射,k是自然数,若f满足(1)uv,uw∈E(G),u≠w,f(uv)≠f(uw);(2)uv∈E(G),C(u)≠C(v).则称f是G的一个邻强边染色,最小的k称为邻强边色数,其中C(u)={f(uv)|uv∈E(G)}.给出了一类3-正则重圈图的邻强边色数. 相似文献
18.
K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*. 相似文献
19.
对简单图G(V,E),设f是从E(G)到{1,2,…,κ}的映射,κ为自然数,如果f满足:1)对任意的uv,uw∈E(G),v≠w,有f(uv)≠f(uw);2)对任意的u,v∈V(G),u≠v,有C(u)≠C(v).则称f为图G的κ-点可区别边染色法,而最小的κ被称为点可区别边色数(其中C(u)={f(uv)|uv∈E(G)}).研究了图K_(2n)\E(K_(2,m))(n≥9,m≥3)的点可区别边色数. 相似文献
20.
对简单图G(V,E),设f是从E(G)到{1,2,…,k}的映射,k为自然数,如果.f满足:1)对任意的uv,uw∈E(G),v≠w,有.f(uv)≠f(uw);2)对任意的u,v∈V(G),u≠v,有C(u)≠C(v).则称f为图G的k-点可区别边染色法,而最小的k被称为点可区别边色数(其中C(u)={f(uv)|uv∈E(G)}.研究了图K_(2n)\E(F_4)(n≥12)的点可区别边色数. 相似文献