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1.
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
2.
Multipliers on Dirichlet Type Spaces 总被引:12,自引:0,他引:12
In this paper, we characterize the pointwise multiplier space M (D
τ, D
μ) of Dirichlet type spaces in the unit ball of C
n
for the values of τ, μ in three cases: (i) τ < 0,μ < 0, (ii) τ < μ, (iii) τ≥μ, τ > n, and construct two functions to show that M(D
τ) ⊂D
τ properly if τ≤n and M(D
τ) ⊂M(D
μ) properly if τ > μ and τ > n− 1.
Supported by the National Natural Science Foundation of China and the National Education Committee Doctoral
Foundation of China 相似文献
3.
Y. Lacroix 《Israel Journal of Mathematics》2002,132(1):253-263
LetG denote the set of decreasingG: ℝ→ℝ withGэ1 on ]−∞,0], and ƒ
0
∞
G(t)dt⩽1. LetX be a compact metric space, andT: X→X a continuous map. Let μ denone aT-invariant ergodic probability measure onX, and assume (X, T, μ) to be aperiodic. LetU⊂X be such that μ(U)>0. Let τ
U
(x)=inf{k⩾1:T
k
xεU}, and defineG
U
(t)=1/u(U)u({xεU:u(U)τU(x)>t),tεℝ We prove that for μ-a.e.x∈X, there exists a sequence (U
n
)
n≥1
of neighbourhoods ofx such that {x}=∩
n
U
n
, and for anyG ∈G, there exists a subsequence (n
k
)
k≥1
withG
U
n
k
↑U weakly.
We also construct a uniquely ergodic Toeplitz flowO(x
∞,S, μ), the orbit closure of a Toeplitz sequencex
∞, such that the above conclusion still holds, with moreover the requirement that eachU
n
be a cylinder set.
In memory of Anzelm Iwanik 相似文献
4.
Ehud Lehrer 《Israel Journal of Mathematics》1987,57(2):239-255
Every ergodic transformation (X, T, ℬ,μ) has an isomorphic system (Y, U,
ν) which is uniquely ergodic and topologically mixing.
This work is a part of an M.Sc. thesis written at The Hebrew University of Jerusalem under the supervision of Professor B.
Weiss to whom the author is greatly indebted. 相似文献
5.
M. I. Gordin 《Journal of Mathematical Sciences》1998,88(1):7-12
Let T be a measure-preserving transformation of a probability space (X, F, μ) and let A be the generator of a μ-symmetric
Markov process with state space X. Under the assumption that A is an “eigenvector” for T an extension of T is constructed
in terms of A. By means of this extension a version of the central limit theorem is proved via approximation by martingales.
Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 10–19.
Translated by V. Sudakov. 相似文献
6.
Bruno de Malafosse 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):189-210
In this paper are given results on the spacesw
τ (μ) andc
τ (μ, μ′) the second one generalizing the well-known spacec
∞ (μ) of sequences that are strongly bounded. Then we deal with matrix transformations into these spaces. These results generalize
those given in [7]. 相似文献
7.
Klaus Schmidt 《Israel Journal of Mathematics》1982,41(1-2):151-153
LetG be a locally compact second countable abelian group, (X, μ) aσ-finite Lebesgue space, and (g, x) →gx a non-singular, properly ergodic action ofG on (X, μ). Let furthermore Γ be the character group ofG and let Sp(G, X) ⊂ Γ denote theL
∞-spectrum ofG on (X, μ). It has been shown in [5] that Sp(G, X) is a Borel subgroup of Γ and thatσ (Sp(G, X))<1 for every probability measureσ on Γ with lim supg→∞Re
(g)<1, where
is the Fourier transform ofσ. In this note we prove the following converse: ifσ is a probability measure on Γ with lim supg→∞Re
(g)<1 (g)=1 then there exists a non-singular, properly ergodic action ofG on (X, μ) withσ(Sp(G, X))=1. 相似文献
8.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
m ? [(L)\tilde]0(t)\mu\in {\tilde L}_0(\tau)
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
[(L)\tilde]0(t){\tilde L}_0(\tau)
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
[(L)\tilde]m(t) é Lm(t) é L#m(t), 1 £ m £ ¥{\tilde L}_m(\tau)\supset L_m(\tau) \supset L^\#_m(\tau), 1\le m\le \infty
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
9.
Consider (X,F, μ,T) a Lebesgue probability space and measure preserving invertible map. We call this a dynamical system. For a subsetA ∈F. byT
A:A →A we mean the induced map,T
A(x)=TrA(x)(x) wherer
A(x)=min{i〉0:T
i(x) ∈A}. Such induced maps can be topologized by the natural metricD(A, A’) = μ(AΔA’) onF mod sets of measure zero. We discuss here ergodic properties ofT
A which are residual in this metric. The first theorem is due to Conze.Theorem 1 (Conze):For T ergodic, T
A is weakly mixing for a residual set of A.Theorem 2:For T ergodic, 0-entropy and loosely Bernoulli, T
A is rank-1, and rigid for a residual set of A.Theorem 3:For T ergodic, positive entropy and loosely Bernoulli, T
A is Bernoulli for a residual set of A.Theorem 4:For T ergodic of positive entropy, T
A is a K-automorphism for a residual set of A.
A strengthening of Theorem 1 asserts thatA can be chosen to lie inside a given factor algebra ofT. We also discuss even Kakutani equivalence analogues of Theorems 1–4. 相似文献
10.
WuJunde 《高校应用数学学报(英文版)》2000,15(4):399-402
Let λ and μ be sequence spaces and have both the signed-weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ. In this paper, it is proved that if λ and μ are β-spaces and λ^β and ,μ^β have also the signed-weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra. 相似文献
11.
We prove a version of Furstenberg’s ergodic theorem with restrictions on return times. More specifically, for a measure preserving
system (X, B, μ,T), integers 0 ≤j <k, andE ⊂X with μ(E) > 0, we show that there existsn ≡ j (modk) with ώ(E ∩T
-nE ∩T
-2nE ∩T
-3nE) > 0, so long asT
k is ergodic. This result requires a deeper understanding of the limit of some nonconventional ergodic averages and the introduction
of a new class of systems, the ‘Quasi-Affine Systems’.
This work was partially carried out while the second author was visiting the Université de Marne la Vallée, supported by NSF
grant 9804651. 相似文献
12.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
13.
Houman Owhadi 《Probability Theory and Related Fields》2003,125(2):225-258
This paper is concerned with the approximation of the effective conductivity σ(A, μ) associated to an elliptic operator ∇
xA
(x,η)∇
x
where for xℝ
d
, d≥1, A(x,η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X, μ). Writing A
N
(x, η) the periodization of A(x, η) on the torus T
d
N
of dimension d and side N we prove that for μ-almost all η
We extend this result to non-symmetric operators ∇
x
(a+E(x, η))∇
x
corresponding to diffusions in ergodic divergence free flows (a is d×d elliptic symmetric matrix and E(x, η) an ergodic skew-symmetric matrix); and to discrete operators corresponding to random walks on ℤ
d
with ergodic jump rates.
The core of our result is to show that the ergodic Weyl decomposition associated to 2(X, μ) can almost surely be approximated by periodic Weyl decompositions with increasing periods, implying that semi-continuous
variational formulae associated to 2(X, μ) can almost surely be approximated by variational formulae minimizing on periodic potential and solenoidal functions.
Received: 10 January 2002 / Revised version: 12 August 2002 / Published online: 14 November 2002
Mathematics Subject Classification (2000): Primary 74Q20, 37A15; Secondary 37A25
Key words or phrases: Effective conductivity – periodization of ergodic media – Weyl decomposition 相似文献
14.
N. T. Peck 《Israel Journal of Mathematics》1971,10(4):397-401
It is proved that for every infinite dimensional normed space (E, ‖ ‖) there is a non-trivial linear space topologyτ onE which is weaker than the norm topology and is such that (E, τ) admits no non-trivial continuous linear functionals. IfE is a space with a generalized basis or is aC(X) space, it is proved that the topologyτ can be taken to be Hausdorff. 相似文献
15.
Under a general hypothesis an expanding map T of a Riemannian manifold M is known to preserve a measure equivalent to the Liouville measure on that manifold. As a consequence of this and Birkhoff’s
pointwise ergodic theorem, the orbits of almost all points on the manifold are asymptotically distributed with regard to this
Liouville measure. Let T be Lipschitz of class τ for some τ in (0,1], let Ω(x) denote the forward orbit closure of x and for a positive real number δ and let E(x0, δ) denote the set of points x in M such that the distance from x0 to Ω is at least δ. Let dim A denote the Hausdorff dimension of the set A. In this paper we prove a result which implies that there is a constant C(T) > 0 such that
dimE(x0,d) 3 dimM - \fracC(T)|logd| \dim E(x_0,\delta) \ge \dim M - \frac{C(T)}{\vert\!\log \delta \vert}
if τ = 1 and
dimE(x0,d) 3 dimM - \fracC(T)log|logd|\dim E(x_0,\delta) \ge \dim M - \frac{C(T)}{\log \vert \log \delta \vert}
if τ < 1. This gives a quantitative converse to the above asymptotic distribution phenomenon. The result we prove is of sufficient
generality that a similar result for expanding hyperbolic rational maps of degree not less than two follows as a special case. 相似文献
16.
Claire Anantharaman-Delaroche 《Israel Journal of Mathematics》2003,137(1):1-33
We show that a measuredG-space (X, μ), whereG is a locally compact group, is amenable in the sense of Zimmer if and only if the following two conditions are satisfied:
the associated unitary representationπ
X ofG intoL
2(X, μ) is weakly contained into the regular representationλ
G and there exists aG-equivariant norm one projection fromL∞(X×X) ontoL∞(X). We give examples of ergodic discrete group actions which are not amenable, althoughπ
X is weakly contained intoλ
G. 相似文献
17.
A local variational relation and applications 总被引:3,自引:0,他引:3
In [BGH] the authors show that for a given topological dynamical system (X,T) and an open coveru there is an invariant measure μ such that infh
μ(T,ℙ)≥h
top(T,U) where infimum is taken over all partitions finer thanu. We prove in this paper that if μ is an invariant measure andh
μ(T,ℙ) > 0 for each ℙ finer thanu, then infh
μ(T,ℙ > 0 andh
top(T,U) > 0. The results are applied to study the topological analogue of the Kolmogorov system in ergodic theory, namely uniform
positive entropy (u.p.e.) of ordern (n≥2) or u.p.e. of all orders. We show that for eachn≥2 the set of all topological entropyn-tuples is the union of the set of entropyn-tuples for an invariant measure over all invariant measures. Characterizations of positive entropy, u.p.e. of ordern and u.p.e. of all orders are obtained.
We could answer several open questions concerning the nature of u.p.e. and c.p.e.. Particularly, we show that u.p.e. of ordern does not imply u.p.e. of ordern+1 for eachn≥2. Applying the methods and results obtained in the paper, we show that u.p.e. (of order 2) system is weakly disjoint from
all transitive systems, and the product of u.p.e. of ordern (resp. of all orders) systems is again u.p.e. of ordern (resp. of all orders).
Project supported by one hundred talents plan and 973 plan. 相似文献
18.
LetX andY beT
1 topological spaces andG(X, Y) the space of all functions with closed graph. Conditions under which the Fell topology and the weak Fell topology coincide
onG(X,Y) are given. Relations between the convergence in the Fell topologyτF, Kuratowski and continuous convergence are studied too. Characterizations of a topological spaceX by separation axioms of (G(X, R), τF) and topological properties of (G(X, R), τF) are investigated. 相似文献
19.
Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) −1). We derive a fast algorithm to compute the coefficients. 相似文献
20.
Christoph Bandt 《Monatshefte für Mathematik》2001,133(4):265-280
Let μ be a self-similar-measure and ν an ergodic shift-invariant measure on a self-similar set A. We show that under weak conditions ν-almost all points x in A show the same local structure, that is, the same tangent measure distribution of μ.
(Received 10 October 2000, in revised form 8 March 2001) 相似文献