共查询到10条相似文献,搜索用时 140 毫秒
1.
Abraham Neyman 《Israel Journal of Mathematics》1981,40(1):54-64
The following conditions on a zonoidZ, i.e., a range of a non-atomic vector measure, are equivalent: (i) the extreme set containing 0 in its relative interior
is a parallelepiped; (ii) the zonoidZ determines them-range of any non-atomic vector measure with rangeZ, where them-range of a vector measure μ is the set ofm-tuples (μ(S
1), …, μ(S
m), whereS
1, …S
m
are disjoint measurable sets and (iii) there is avector measure space (X, Σ, μ) such that any finite factorization ofZ, Z =ΣZ
i
, in the class of zonoids could be achieved by decomposing (X, Σ). In the case of ranges of non-atomic probability measures (i) is automatically satisfied, so (ii) and (iii) hold.
Partially supported by NSF grant MCS-79-06634 相似文献
2.
Let (Ω,Σ,μ) be a measure space and letP be an operator onL
2(Ω,Σ,μ) with ‖P‖≦1,Pf≧0 a.e. wheneverf≧0. If the subspaceK is defined byK={x| ||P
n
x||=||P
*n
x||=||x||,n=1,2,...} thenK=L
2(Ω,Σ1,μ), where Σ1 ⊂ Σ and onK the operatorP is “essentially” a measure preserving transformation. Thus the eigenvalues ofP of modulus one, form a group under multiplication.
This last result was proved by Rota for finiteμ here finiteness is not assumed) and is a generalization of a theorem of Frobenius and Perron on positive matrices.
The research reported in this document has been sponsored in part by Air Force Office of Scientific Research, OAR through
the European Office, Aerospace Research, United States Air Force. 相似文献
3.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
4.
Daniel Wulbert 《Israel Journal of Mathematics》2001,126(1):363-380
LetX be a Borel subset of a separable Banach spaceE. Letμ be a non-atomic,σ-finite, Borel measure onX. LetG ⊆L
1 (X, Σ,μ) bem-dimensional.
Theorem:There is an l ∈ E* and real numbers −∞=x
0<x
1<x
2<…<x
n<x
n+1=∞with n≤m, such that for all g ∈ G,
相似文献
5.
In this paper, we shall give a necessary and sufficient condition for which the dual of Λ
ω
p
(X, M, μ) (0<p<∞) is zero, and a necessary and sufficient condition for which Λ
ω
p
(X, M, μ), (0<p<1) is normable.
Supported by 973 project (G1999075105), RFDP (20030335019) and ZJNSF(RC97017). 相似文献
6.
Summary This paper is concerned with second order differential systems involving two parameters with boundary conditions specified
at three points. In particular, we consider the system y' = k(x, λ, μ)z, z' = -g(x, λ, μ)y, where k and g are real-valued
junctions defined on X: a ≤ x ≤ c, L: L1 < λ < L2, and M: M1 < μ < M2. This system is studied together with the boundary conditions α(λ, μ)y(a) - β(λ, μ)z(a)=0, γ(λ, μ)y(b) - δ(λ, μ)z(b)=0, ε1(μ)y(b) - φ1(μ)z(b)=ε2(μ)y(c) - φ2(μ)z(c), where α, β, δ, γ, εi, φi, i=1, 2, are continuous functions of the parameters. This work establishes the existence of eigenvalue pairs for the boundary
problem and the oscillatory behavior of the associated solutions. These results complement those previously obtained by the
authors and B. D. Sleeman, where boundary conditions of the ? Sturm-Liouville ? type were studied.
Entrata in Redazione il 5 dicembre 1977.
The research for this paper was supported by a University College Reasearch Grant, University of Alabama in Birmingham. 相似文献
7.
Ofelia T. Alas Salvador Hernández Manuel Sanchis Michael G. Tkachenko Richard G. Wilson 《Acta Mathematica Hungarica》2006,112(3):199-219
Summary We study subposets of the lattice L_1(X) of all T1-topologies on a set X, namely Σt(X), Σ3(X) and Σlc(X), being respectively the collections of all Tychonoff, all T3 and all locally compact Hausdorff topologies on X, with a view to deciding which elements of these partially ordered sets have and which do not have covers, that is to say
immediate successors, in the respective posets. In the final section we discuss the subposet Σ G of all Hausdorff group topologies on a group G. 相似文献
8.
B. Farkas 《Acta Mathematica Hungarica》2003,98(1-2):71-77
Given a measure space < Ω,m,μ >, a locally bounded, Hausdorff topological linear space < X, τ > and a real number 0<p<1, one can define the space Lp(Ω,m,μ,X), which is, under certain assumptions, a Fréchet space if endowed with a suitable topology. M.M. Day [1] has given a necessary
and sufficient condition, in terms of the properties of the measure space < Ω,m,μ >, for the dual of Lp(Ω,m,μ,C) to be trivial. In this paper a different proof along with a slight generalization is given for this result, using standard
and elementary measure theoretic arguments.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
M. I. Gordin 《Journal of Mathematical Sciences》2000,99(2):1053-1060
Let T: X→X be an automorphism (a measurable invertible measure-preserving transformation) of a probability space (X, F, μ)
and let two μ-symmetric Markov generators Au and As acting on the space L2=L2 (X, F, μ) be “eigenfunctions” of the automorphism T with eigenvaluesθ
u
> 1 andθ
s
< 1, respectively. We construct an extension of the automorphism T having increasing and decreasing filtrations by means
of a transformation on the path space of these processes. Under additional conditions, we give an estimate of the maximal
correlation coefficient between the δ-fields chosen from these filtrations. Hyperbolic toral automorphisms are considered
as an example. Applications to limit theorems are given. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 61–72.
Translated by M. I. Gordin. 相似文献
10.
For given analytic functions ϕ(z) = z + Σ
n=2∞ λ
n
z
n
, Ψ(z) = z + Σ
n=2∞ μ with λ
n
≥ 0, μ
n
≥ 0, and λ
n
≥ μ
n
and for α, β (0≤α<1, 0<β≤1), let E(φ,ψ; α, β) be of analytic functions ƒ(z) = z + Σ
n=2∞
a
n
z
n
in U such that f(z)*ψ(z)≠0 and
for z∈U; here, * denotes the Hadamard product. Let T be the class of functions ƒ(z) = z - Σ
n=2∞|a
n
| that are analytic and univalent in U, and let E
T
(φ,ψ;α,β)=E(φ,ψ;α,β)∩T. Coefficient estimates, extreme points, distortion properties, etc. are determined for the class E
T
(φ,ψ;α,β) in the case where the second coefficient is fixed. The results thus obtained, for particular choices of φ(z) and ψ(z), not only generalize various known results but also give rise to several new results.
University of Bahrain, Isa Town, Bahrain. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1162–1170,
September, 1997. 相似文献