共查询到20条相似文献,搜索用时 250 毫秒
1.
Guang Gui DING 《数学学报(英文版)》2005,21(5):1045-1048
In this paper we give the sufficient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no e-isometry from 1 any abstract M space with a strong unit into C0(Г) if 0 〈 e 〈 1/9. 相似文献
2.
《数学研究与评论》1984,(3)
§1 The main result The classical Rao-Blackwell-Lehmann-Scheffe theorm guarantees the existence of uniform minimum variance unbiased estimate (UMVUE) for any estimable parameterfunctions, in case there is a sufficient and complete statistic. The situation becomes complicated when such statistics do not exist. For example, UMVUE does not exist for a function g of the parameter of the family 相似文献
3.
In this paper the authors give a new integral estimate of the Bessel function,which is an extension of Calder(?)n-Zygmund's result.As an application of this result,we prove that the parameterized Marcinkiewicz integralμ_Ω~p with variable kernels is of type (2,2),where the kernel functionΩdoes not have any smoothness on the unit sphere in R~n. 相似文献
4.
The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p(R^n),P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p(R^n) into weak Lμ^p(R^n),1≤p〈∞. 相似文献
5.
林诒勋 《高校应用数学学报(英文版)》1993,8(1):76-85
The main goal of this paper is to study the following combinatorial problem.given a finite set E={e1,e2,…em} and a subset familly σ={S1,S2,…,Sn}of E,does there exist a tree T with the edge set E such that each induced subgraph T[Si] of Si is precisely a path (1≤i≤k)? 相似文献
6.
Let t ≥ 2 be an integer, and let _(p_1, ···, p_t)be distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Z_(p_1p_2···p_t)and the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Z_(p_1p_2···p_t). 相似文献
7.
LUSTERNIK-SCHNIRELMANN CATEGORY AND EMBEDDING FINITE
COVERING MAPS, PRINCIPAL G-BUNDLES INTO BUNDLES
Liu Luofei 《数学年刊B辑(英文版)》1996,17(3):317-324
The author proves several embedding theorems for finite covering maps,principal G-bundies into bundles.The main results are 1. Let π:E→X be a finite covering map, and X a connected locally path-connected paracompact space. If cat X≤k, then the finite covering space π:E→X can be embedded into the trivial real k-plane bundle. 2. Let π:E→X be a principal G-bundle over a paracompact space. If there exists a linera action of Gon F(F=R or C)and cat X≤k ,then π:E→X can be embedded into ξ1 … ξn for any F-vector bundles ξi,i=1,…k. 相似文献
8.
GuangGuiDING 《数学学报(英文版)》2003,19(4):793-800
In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too. 相似文献
9.
Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable. 相似文献
10.
Tang Qi 《数学年刊B辑(英文版)》1991,12(3):309-317
Giving a nonisotropic plasticity problem on a Sobolev Space, the author tries to relax it to a new problem whioh is posed on a subset of BD (Ω). It is proved that this relaxation does not change the equilibrium energy and that the solutions exist in such settings under not too restricted conditions. 相似文献
11.
The object of this paper is to prove the following theorem: Let Y be a closed subspace of the Banach space X, (S,Σ,μ) a σ-finite measure space, L(S,Y) (respectively, L(S, X)) the space of all strongly measurable functions from S to Y (respectively, X), and p a positive number. Then L(S,Y) is pointwise proximinal in L(S,X) if and only if Lp(μ,Y) is proximinal in Lp(μ,X). As an application of the theorem stated above, we prove that if Y is a separable closed subspace of the Banach space X, p is a positive number, then Lp(μ,Y) is proximinal in Lp(μ,X) if and only if Y is proximinal in X. Finally, several other interesting results on pointwise best approximation are also obtained. 相似文献
12.
The object of this paper is to prove the following theorem: If Y is a closed subspace of the Banach space X, then L1(μ, Y) is proximinal in L1(μ, X) if and only if Lp(μ, Y) is proximinal in Lp(μ, Y) for every p, 1 < p < ∞. As an application of this result we prove that if Y is either reflexive or Y is a separable proximinal dual space, then L1(μ, Y) is proximinal in L1(μ, X). 相似文献
13.
Let Ω be a plane bounded region. Let U = {Uμ(P):μ(P)εL∞(Ω), uμ ε H22, 0(Ω) and a(P, μ(P))uμ,xx + 2b(P, μ(P))uμ,xy + c(P, μ(P))uμ,vv = ƒ(P) for P ε Ω; here we are given a(P, X), b(P, X), c(P, X) ε L∞(Ω × E1), ƒ(P) ε Lp(Ω) with p > 2, and our partial differential equation is uniformly elliptic. The functions μ(P) are called profiles. We establish sufficient conditions—which when they apply are constructive—that there exist a μ0 ε L∞(Ω) such that uμ0 (P) uμ(P) for all P ε Ω and for each μ ε L∞(Ω). Similar results are obtained for a difference equation and convergence is proved. 相似文献
14.
Richard Arens Moshe Goldberg W. A. J. Luxemburg 《Journal of Mathematical Analysis and Applications》1992,170(2)
Let S be a seminorm on an algebra
. In this paper we study multiplicativity and quadrativity factors for S, i.e., constants μ > 0 and λ > 0 for which S(xy) μS(x)S(y) and S(x2) λS(x)2 for all x, y A. We begin by investigating quadrativity factors in terms of the kernel of S. We then turn to the question, under what conditions does S have multiplicativity factors if it has quadrativity factors? We show that if
is commutative then quadrativity factors imply multiplicativity factors. We further show that in the noncommutative case there exist both proper seminorms and norms that have quadrativity factors but no multiplicativity factors. 相似文献
15.
We show that for every Borel-measurable mapping Δ: [ω]ω →
there exists A [ω]ω and there exists a continuous mapping Γ: [A]ω → [A]ω with Γ(X) X such that for all X, Y [A]ω it follows that Δ(X) = Δ(Y) if Γ(X) = Γ(Y). In a sense, this is generalization of the Erdös-Rado canonization theorem 相似文献
16.
Let X be a Banach space, (Ω,Σ,μ) a finite measure space, and L1(μ,X) the Banach space of X-valued Bochner μ-integrable functions defined on Ω endowed with its usual norm. Let us suppose that Σ0 is a sub-σ-algebra of Σ, and let μ0 be the restriction of μ to Σ0. Given a natural number n, let N be a monotonous norm in . It is shown that if X is reflexive then L1(μ0,X) is N-simultaneously proximinal in L1(μ,X) in the sense of Fathi et al. [Best simultaneous approximation in Lp(I,E), J. Approx. Theory 116 (2002), 369–379]. Some examples and remarks related with N-simultaneous proximinality are also given. 相似文献
17.
M. R. Dostanic 《Mathematical Notes》2005,77(5-6):777-786
In this paper, the norm of the Cauchy transform C is obtained on the space L
2(D, dμ), where dμ = ω(|z|) dA(z). Also, (for the case ω ≡ 1), the first regularized trace of the operator C* C on L
2(Ω) is obtained. The results are illustrated by examples, with different specific choices of the function ω and the domain Ω.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 844–853.Original Russian Text Copyright ©2005 by M. R. Dostanic. 相似文献
18.
On a simplex SRd, the best polynomial approximation is En()Lp(S)=Inf{Pn−Lp(S): Pn of total degree n}. The Durrmeyer modification, Mn, of the Bernstein operator is a bounded operator on Lp(S) and has many “nice” properties, most notably commutativity and self-adjointness. In this paper, relations between Mn−z.dfnc;Lp(S) and E[√n]()Lp(S) will be given by weak inequalities will imply, for 0<α<1 and 1≤p≤∞, En()Lp(S)=O(n-2α)Mn−z.dfnc;Lp(S)=O(n-α). We also see how the fact that P(D)εLp(S) for the appropriate P(D) affects directional smoothness. 相似文献
19.
In a previous paper [H. Tsuiki, Y. Hattori, Lawson topology of the space of formal balls and the hyperbolic topology of a metric space, Theoret. Comput. Sci. 405 (2008) 198–205], the authors introduced the hyperbolic topology on a metric space, which is weaker than the metric topology and naturally derived from the Lawson topology on the space of formal balls. In this paper, we characterize spaces Lp(Ω,Σ,μ) on which the hyperbolic topology induced by the norm p coincides with the norm topology. We show the following:
- (1) The hyperbolic topology and the norm topology coincide for 1<p<∞.
- (2) They coincide on L1(Ω,Σ,μ) if and only if μ(Ω)=0 or Ω has a finite partition by atoms.
- (3) They coincide on L∞(Ω,Σ,μ) if and only if μ(Ω)=0 or there is an atom in Σ.
Keywords: Normed linear space; Lp; Uniformly rotund (convex); Locally uniformly rotund (convex); Atom; Metric space; Hyperbolic topology; Norm topology; Formal ball; Lawson topology 相似文献
20.
Dalibor Volný Benjamin Weiss 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2004,40(6):771-778
Let T be an ergodic automorphism of a probability space, f a bounded measurable function, . It is shown that the property that the probabilities μ(|Sn(f)|>n) are of order n−p roughly corresponds to the existence of an approximation in L∞ of f by functions (coboundaries) g−g○T, gLp. Similarly, the probabilities μ(|Sn(f)|>n) are exponentially small iff f can be approximated by coboundaries g−g○T where g have finite exponential moments.