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1.
Let T(Δ) and B(Δ) be the Teichmüller space and the infinitesimal Teichmüller space of the unit disk Δ respectively. In this paper, we show
that [ν]
B(Δ) being an infinitesimal Strebel point does not imply that [ν]
T(Δ) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved.
This work was supported by the National Natural Science Foundation of China (Grant No. 10571028) 相似文献
2.
Let B denote a separable Banach space with norm ‖⋅‖, and let μ be a probability measure on B for which linear functionals have mean zero and finite variance. Then there is a Hilbert space H
μ
determined by the covariance of μ such that H
μ
⊆B. Furthermore, for all ε>0 and x in the B-norm closure of H
μ
, there is a unique point, T
ε
(x), with minimum H
μ
-norm in the B-norm ball of radius ε>0 and center x. If X is a random variable in B with law μ, then in a variety of settings we obtain the central limit theorem (CLT) for T
ε
(X) and certain modifications of such a quantity, even when X itself fails the CLT. The motivation for the use of the mapping T
ε
(⋅) comes from the large deviation rates for the Gaussian measure γ determined by the covariance of X whenever γ exists. However, this is only motivation, and our results apply even when this Gaussian law fails to exist.
Research partially supported by NSA Grant H98230-06-1-0053. 相似文献
3.
Na SUN 《数学学报(英文版)》2007,23(10):1909-1914
In this paper, we introduce an operator Hμ(z) on L^∞(△) and obtain some of its properties. Some applications of this operator to the extremal problem of quasiconformal mappings are given. In particular, a sufficient condition for a point r in the universal Teichmfiller space T(△) to be a Strebel point is obtained. 相似文献
4.
Let [A, a] be a normed operator ideal. We say that [A, a] is boundedly weak*-closed if the following property holds: for all Banach spaces X and Y, if T: X → Y** is an operator such that there exists a bounded net (T
i
)
i∈I
in A(X, Y) satisfying lim
i
〈y*, T
i
x
y*〉 for every x ∈ X and y* ∈ Y*, then T belongs to A(X, Y**). Our main result proves that, when [A, a] is a normed operator ideal with that property, A(X, Y) is complemented in its bidual if and only if there exists a continuous projection from Y** onto Y, regardless of the Banach space X. We also have proved that maximal normed operator ideals are boundedly weak*-closed but, in general, both concepts are different.
相似文献
5.
S. S. Podkorytov 《Journal of Mathematical Sciences》2011,175(5):609-619
Homotopy classes of mappings of a space X to the circle T form an Abelian group B(X) (the Bruschlinsky group). If a: X → T is a continuous mapping, then [a] denotes the homotopy class of a, and I
r
(a): (X × T)
r
→
\mathbbZ \mathbb{Z} is the indicator function of the rth Cartesian power of the graph of a. Let C be an Abelian group and let f: B(X) → C be a mapping. By definition, f has order not greater than r if the correspondence I
r
(a) → f([a]) extends to a (partly defined) homomorphism from the Abelian group of Z-valued functions on (X × T)
r
to C. It is proved that the order of f equals the algebraic degree of f. (A mapping between Abelian groups has degree at most r if all of its finite differences of order r +1 vanish.) Bibliography: 2 titles. 相似文献
6.
Iwo Labuda 《Positivity》2010,14(4):801-813
Let μ be a measure from a σ-algebra of subsets of a set T into a sequentially complete Hausdorff topological vector space X. Assume that μ is convexly bounded, i.e., the convex hull of its range is bounded in X, and denote by L
1(μ) the space of scalar valued functions on T which are integrable with respect to the vector measure μ. We study the inheritance of some properties from X to L
1(μ). We show that the bounded multiplier property passes from X to L
1(μ). Answering a 1972 problem of Erik Thomas, we show that for a rather large class of F-spaces X the non-containment of c
0 passes from X to L
1(μ). 相似文献
7.
It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. 相似文献
8.
Let X be a Banach space, K be a scattered compact and T: B
C(K) → X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B
C(K)** → X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either
is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C
1,u
-smooth noncompact operator from B
c
O which does not fix any (affine) basic sequence.
P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503. 相似文献
9.
10.
Domingo Pestana José M. Rodríguez José M. Sigarreta María Villeta 《Central European Journal of Mathematics》2012,10(3):1141-1151
If X is a geodesic metric space and x
1; x
2; x
3 ∈ X, a geodesic triangle T = {x
1; x
2; x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of
degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs. 相似文献
11.
Let (X, d) be a compact metric space and let (X) denote the space of all finite signed Borel measures on X. Define I: (X) → ℝ by I(μ) = ∫
X
∫
X
d(x, y)dμ(x)dμ(y), and set M(X) = sup I(μ), where μ ranges over the collection of measures in (X) of total mass 1. The space (X, d) is quasihypermetric if I(μ) ≦ 0 for all measures μ in (X) of total mass 0 and is strictly quasihypermetric if in addition the equality I(μ) = 0 holds amongst measures μ of mass 0 only for the zero measure.
This paper explores the constant M(X) and other geometric aspects of X in the case when the space X is finite, focusing first on the significance of the maximal strictly quasihypermetric subspaces of a given finite quasihypermetric
space and second on the class of finite metric spaces which are L
1-embeddable. While most of the results are for finite spaces, several apply also in the general compact case. The analysis
builds upon earlier more general work of the authors [11] [13].
相似文献
12.
If X is a geodesic metric space and x
1,x
2,x
3 ∈ X, a geodesic triangle
T = {x
1,x
2,x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. $\delta(X)=\inf\{\delta\ge 0: \, X \, \text{ is $\delta(X)=\inf\{\delta\ge 0: \, X \, \text{ is In this paper we relate the hyperbolicity constant of a graph with some known parameters of the graph, as its independence
number, its maximum and minimum degree and its domination number. Furthermore, we compute explicitly the hyperbolicity constant
of some class of product graphs. 相似文献
13.
I. Juhász 《Israel Journal of Mathematics》1993,81(3):369-379
The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT
2 withω(X)≥κ then some λ withκ≤λ≤2<κ is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω
1, and thus solves problem 22 of [M]. Also, it is consistent with 2ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT].
Research supported by OTKA grant no. 1908. 相似文献
14.
G. Schlüchtermann 《manuscripta mathematica》1991,73(1):397-409
A sufficient condition is given when a subspaceL⊂L
1(μ,X) of the space of Bochner integrable function, defined on a finite and positive measure space (S, Φ, μ) with values in a Banach spaceX, is locally uniformly convex renormable in terms of the integrable evaluations {∫
A
fdμ;f∈L}. This shows the lifting property thatL
1(μ,X) is renormable if and only ifX is, and indicates a large class of renormable subspaces even ifX does not admit and equivalent locally uniformly convex norm. 相似文献
15.
Andrés del Junco 《Israel Journal of Mathematics》1998,104(1):301-320
An ergodic measure-preserving transformationT of a probability space is said to be simple (of order 2) if every ergodic joining λ ofT with itself is eitherμ×μ or an off-diagonal measureμ
S
, i.e.,μ
S
(A×B)=μ(A∩S
;−n
;B) for some invertible, measure preservingS commuting withT. Veech proved that ifT is simple thenT is a group extension of any of its non-trivial factors. Here we construct an example of a weakly mixing simpleT which has no prime factors. This is achieved by constructing an action of the countable Abelian group ℤ⊕G, whereG=⊕
i=1
∞
ℤ2, such that the ℤ-subaction is simple and has centralizer coinciding with the full ℤ⊕G-action. 相似文献
16.
We study Karhunen-Loève expansions of the process(X
t
(α))
t∈[0,T) given by the stochastic differential equation $
dX_t^{(\alpha )} = - \frac{\alpha }
{{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)
$
dX_t^{(\alpha )} = - \frac{\alpha }
{{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)
, with the initial condition X
0(α) = 0, where α > 0, T ∈ (0, ∞), and (B
t
)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X
(α). As applications, we calculate the Laplace transform and the distribution function of the L
2[0, T]-norm square of X
(α) studying also its asymptotic behavior (large and small deviation). 相似文献
17.
Résumé Soit X un processus gaussien stationnaire non dérivable. Nous étudions le nombre de passages en zéro du processus régularisé par
convolution. Sous des hypothèses peu restrictives sur X, cette variable convenablement normalisée, converge au sens de L
2 quand la taille du filtre tend vers zéro. Lorsque X admet un temps local continu, la limite obtenue est le temps local.
Summary Let {X(t)} be a stationary non differentiable Gaussian process and let ϕɛ(u=ɛ−1 ϕ(u/ɛ) be an approximate identity. Setting X ɛ(t)=X*ϕɛ(t) and letting N ɛ(T) be the number of zeros of X ɛ in the interval [0, T] it is shown that under weak technical conditions there are constants C(ɛ) so that C(ɛ) N ɛ(T) converges in L 2 as ɛ→0. When X admits a continuous local time, the limit is the local time L(0, T) at zero of X(t).相似文献
18.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献
19.
Mohan Joshi 《Proceedings Mathematical Sciences》1980,89(2):95-100
Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT
-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT
-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation. 相似文献
20.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1999,109(1):75-85
For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L
1 (μ), X) has denting points iffL
1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit
ball of ℓ(X, Y) are strongly extreme points. 相似文献