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61.
The bicompletion of an asymmetric normed linear space 总被引:5,自引:0,他引:5
A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖s) is a Banach space, where ‖x‖s= max {‖x‖,‖-x‖} for all x∈X. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖Y). Furthermore the space (Y,‖·‖Y) is unique (up to isometric isomorphism).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
62.
It is proved that for any Fuchsian group Γ such that ℍ/Γ is a hyperbolic Riemann surface, the Teichmüller curve V(Γ) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Γ) onto V(Γ) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmüller curves is deduced, which generalizes
a classical result that the Teichmüller curve V(Γ) depends only on the type of Γ and not on the orders of the elliptic elements of Γ when ℍ/Γ is a compact hyperbolic Riemann
surface. 相似文献
63.
Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π0(Homeo(M))→Out π1(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau. 相似文献
64.
设Gi是满足第二可数性公理的、Hausdorff的、顺从的、r-离散的、主的局部紧群胚,并且有一个紧开G-集覆盖;设Pi是Gi中含G_i ̄0的开闭集,且满足及相应的模是具有性质DC的C(Gi)的子代数(i=1,2).本文证明从A(P1)到A(P2)上的每一个等距代数同构可以扩张成从C(G1)到C(G2)上的C-同构,进一步,可以对C(G2)重新坐标化,使得这个C-同构可由一个群胚同构生成. 相似文献
65.
杨爱珍 《应用数学与计算数学学报》1998,12(2):39-45
本文不仅给出一种构造局部性好的正交小波基的方法,并且给出了构造各种优良性质的正交小波基的一般思想方法。其特点:使构造的小波母函数有具体的表达式,既有较好的光滑性,又有很好的局部性,并且其收敛速度与│t│~(-(3k 1))同阶,其中k为任意自然数。这种方法不需要每次重新构造函数,只要改变k的值,就能满足不同实际问题的需要。 相似文献
66.
Let q be a prime power, ??q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over ??q, with two vertices (p1, p2) ∈ P and [ l1, l2] ∈ L being adjacent if and only if p2 + l2 = pl. We prove that graphs Gq(k, m) and Gq′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q ? 1), gcd (m, q ? 1)} = {gcd (k′, q ? 1),gcd (m′, q ? 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005 相似文献
67.
Let G be a locally compact group with a fixed right Haar measure andX a separable Banach space. LetL
p
(G, X) be the space of X-valued measurable functions whose norm-functions are in the usualL
p
. A left multiplier ofL
p
(G, X) is a bounded linear operator onB
p
(G, X) which commutes with all left translations. We use the characterization of isometries ofL
p
(G, X) onto itself to characterize the isometric, invertible, left multipliers ofL
p
(G, X) for 1 ≤p ∞,p ≠ 2, under the assumption thatX is not thel
p
-direct sum of two non-zero subspaces. In fact we prove that ifT is an isometric left multiplier ofL
p
(G, X) onto itself then there existsa y ∃ G and an isometryU ofX onto itself such thatTf(x) = U
(R
y
f)(x). As an application, we determine the isometric left multipliers of L1 ∩L
p
(G, X) and L1 ∩C
0
(G, X) whereG is non-compact andX is not the lp-direct sum of two non-zero subspaces. If G is a locally compact abelian group andH is a separable Hubert space, we define
where г is the dual group of G. We characterize the isometric, invertible, left multipliers ofA
p
(G, H), provided G is non-compact. Finally, we use the characterization of isometries ofC(G, X) for G compact to determine the isometric left multipliers ofC(G, X) providedX
*
is strictly convex. 相似文献
68.
Let Möb(Sn+1) denote the Möbius transformation group of Sn+1. A hypersurface f:Mn → Sn+1 is called a Möbius homogeneous hypersurface, if there exists a subgroup G ? Möb(Sn+1) such that the orbit G(p)={φ(p)|φ ∈ G}=f(Mn), p ∈ f(Mn). In this paper, we classify the Möbius homogeneous hypersurfaces in Sn+1 with at most one simple principal curvature up to a Möbius transformation. 相似文献
69.
Osamu Hatori Takeshi Miura Hiroyuki Takagi 《Proceedings of the American Mathematical Society》2006,134(10):2923-2930
Let be a surjective mapping from a uniform algebra on a compact Hausdorff space onto a uniform algebra on a compact Hausdorff space . Suppose that holds for every . Then we have that is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).
70.
Don Coppersmith Nick Howgrave-Graham Phong Q. NguyêÜn Igor E. Shparlinski 《Journal of Discrete Algorithms》2006,4(2):324-335
Given two k element subsets , we give a quasi-linear algorithm to either find such that S=λT or prove that no such λ exists.This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature. 相似文献