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1.
LetT be a Markov operator onL
1(X, Σ,m) withT*=P. We connect properties ofP with properties of all productsP ×Q, forQ in a certain class: (a) (Weak mixing theorem)P is ergodic and has no unimodular eigenvalues ≠ 1 ⇔ for everyQ ergodic with finite invariant measureP ×Q is ergodic ⇔ for everyu ∈L
1 with∝ udm=0 and everyf ∈L
∞ we haveN
−1Σ
n
≠1/N
|<u, P
nf>|→0. (b) For everyu ∈L
1 with∝ udm=0 we have ‖T
nu‖1 → 0 ⇔ for every ergodicQ, P ×Q is ergodic. (c)P has a finite invariant measure equivalent tom ⇔ for every conservativeQ, P ×Q is conservative. The recent notion of mild mixing is also treated.
Dedicated to the memory of Shlomo Horowitz
An erratum to this article is available at . 相似文献
2.
In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L(logL)a(E1 × E2) for some a 〉 0, which is optimal. 相似文献
3.
Let Ω⊂R
n
(n≥2) be a bounded open set;Q
T
=Ω×[0,T],S
T
=δΩ×[0,T],S
1,S
2 be the partial boundaries of Ω andS
1∪S
2=δΩ,S
1∩S
2=Φ. We denote Γ1.T
=S
1×[0,T], Γ2.T
=S
2×[0,T], and consider the problem
相似文献
4.
Jiang Liya Chen Jiecheng 《高校应用数学学报(英文版)》2006,21(1):69-78
The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i|x|^aΩ(x)|x|^-n is studied,where a∈R,a≠0,1 and Ω∈L^1(S^n-1) is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω(x' )∈Llog+L(S^n-1 ), the Fp^a,q(R^n) boundedness of the above operator is obtained. Meanwhile ,when Ω(x) satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 (R^n). 相似文献
5.
In this paper we consider a convolution operator Tf=p.v. Ω * f with Ω(x)=K(x)×eiλh(x), λ>0, where K(x) is a weak Calderón-Zygmund kernel and h(x) is a real-valued differentiable function. We give a boundedness
criterion for such an operator to map the Besov space B
1
0.1
(Rn) into itself.
This research was partially supported by NNSF and NEC in P. R. China. 相似文献
6.
This paper deals with the blow-up properties of solutions to a system of heat equations u
t=Δu, v
t=Δv in B
R×(0, T) with the Neumann boundary conditions εu/εη=e
v, εv/εη=e
u on S
R×[0, T). The exact blow-up rates are established. It is also proved that the blow-up will occur only on the boundary.
This work is supported by the National Natural Science Foundation of China 相似文献
7.
Letx
1, x2, ..., xNbep×1 random vectors distributed independently asN(u, Σ), Σ>0;u and Σ are unknown. In this paper, we derive the exact non-null distribution of Wilks' likelihood ratio criterion,L
VC, for testingH:∑=σ
2[(1−ρ)I+ρee′], σ>0 and ρ are unknown against the alternativeA≠H,e′=(1, 1, …, 1): 1×p. The distribution has been derived in three series forms: (1) a series of Meijer'sG-functions through Mellin transform, (2) an, alternate series using contour, intergration and (3) a series of chi square distributions.
Powers have been computed based on these forms of the distribution forp=2 and 3. 相似文献
8.
Mustapha Mokhtar-Kharroubi 《Journal of Evolution Equations》2008,8(2):327-352
We deal with streaming operators T
H
defined in L
1 spaces by the directional derivative with positive boundary operator H of norm 1 relating the incoming and outgoing fluxes. It is known that T
H
need not be a generator but there exists a contraction semigroup generated by an extension A of T
H
. This paper deals with the total mass carried by individual trajectories {e
tA
f; t ≥ 0} for nonnegative initial data f and related topics. In particular, our analysis covers the problem of (the lack of) stochasticity of {e
tA
; t ≥ 0} for conservative boundary operator H.
相似文献
9.
Let (S)⊄L
2(S′(∔),μ)⊄(S)* be the Gel'fand triple over the white noise space (S′(∔),μ). Let (e
n
,n>-0) be the ONB ofL
2(∔) consisting of the eigenfunctions of the s.a. operator
. In this paper the Euler operator Δ
E
is defined as the sum
, where ∂
i
stands for the differential operatorD
e
i. It is shown that Δ
E
is the infinitesimal generator of the semigroup (T
t
), where (T
t
ϕ)(x)=ϕ(e
t
x) for ϕ∈(S). Similarly to the finite dimensional case, the λ-order homogeneous test functionals are characterized by the Euler equation:
Δ
Eϕ
=λϕ. Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
Supported by the National Natural Science Foundation of China. 相似文献
10.
Paulo Leandro Dattori da Silva 《Annali di Matematica Pura ed Applicata》2010,189(3):403-413
This paper deals with semi-global C k -solvability of complex vector fields of the form ${\mathsf{L}=\partial/\partial t+x^r(a(x)+ib(x))\partial/\partial x,}
11.
In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” uf (·, T) is studied, where uf (x,t) is the solution of the initial boundary-value problem utt−Δu=0 in Ω×(0,T), u|t<0=0, u|∂Ω×(0,T)=f, and the (singular) control f runs over the class L2((0,T); H−m (∂Ω)) (m>0). The following result is established. Let ΩT={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝn (diam Ω<∞) filled with waves by a final instant of time t=T, let T*=inf{T : ΩT=Ω} be the time of filling the whole domain Ω. We introduce the notation Dm=Dom((−Δ)m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H2(Ω)∩H
0
1
(Ω);D−m=(Dm)′;D−m(ΩT)={y∈D−m:supp y ⋐ ΩT. If T<T., then the reachable set R
m
T
={ut(·, T): f ∈ L2((0,T), H−m (∂Ω))} (∀m>0), which is dense in D−m(ΩT), does not contain the class C
0
∞
(ΩT). Examples of a ∈ C
0
∞
, a ∈ R
m
T
, are presented.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21.
Translated by T. N. Surkova. 相似文献
12.
Eli Glasner 《Journal d'Analyse Mathématique》1994,64(1):241-262
For a minimal distal flow (X, T) and a positive integern, let be the largest distal factor of ordern. The existence of a denseG
δ subset ω ofX is shown, such that forx ∈ ω the orbit closure of (x,x,...,x) ∈ X
n+1 under τ =T ×T
2 ... ×T
n+1 is π-saturated. In fact, an analogous statement for a general minimal flow is proved in terms of its PI-tower. On the way
we get some topological “ergodic” decomposition theorems. 相似文献
13.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
14.
H. H. Schaefer 《Israel Journal of Mathematics》1984,48(2-3):196-204
Let (X, Σ, μ) be a σ-finite measure space,T a compact irreducible (positive, linear) operator onL
p (μ) (1≦p<+∞). It is shown that the spectral radiusr ofT is characterized by the minimax property {fx196-1} where ∑0 denotes the ring of sets of finite measure and whereQ denotes the set of all, almost everywhere positive functions inL
p. Moreover, ifr>0 then equality on either side is assumed ifff is the (essentially unique) positive eigenfunction ofT. Various refinements are given in terms of corresponding relations for irreducible finite rank operators approximatingT.
Dedicated to H. G. Tillmann on his 60th birthday 相似文献
15.
We consider direct productsS×UeεE
G
e=S
1×…×S
n × UeεE
G
e of non-group finite cyclic semigroupsS
i, 1 ≤i ≤n, and finite unions of finite groups UeεE
G
e We prove that if such a semigroup is isomorphic to another of the same form, sayT×U
fεF
H
f
=T
1×…×U
fεF
H
f
, whereT
j
are non-group cyclic semigroups, 1≤j≤l, and U
fεF
H
f
is a union of groups, thenS is isomorphic toT and UeεE
G
e is isomorphic to UfεF
H
f
. We then determine when a finite semigroup has such a decomposition and show how the direct factors can be found. 相似文献
16.
Zhu Xuexian 《分析论及其应用》1989,5(3):83-92
We show that if K(x,y)=Ω(x,y)/|x|n|y|m is a Calder n-Zygmund kerned on Rn×Rm, where Ω∈L2(Sn−1×Sm−1) and b(x,y) is any bounded function which is radial with x∈Rn and y∈Rm respectively, then b(x,y)K(x,y) is the kernel of a convolution operator which is bounded on Lp(Rn×Rm) for 1<p<∞ and n≧2, m≧2.
Project supported by NSFC 相似文献
17.
Jiao Yulan 《分析论及其应用》2004,20(4):373-382
Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 <α≤ 1) and implies the Lp(Rn) (1 < p < oo) boundedness for the operator TA. Some endpoint estimates are also established. 相似文献
18.
Takafumi Isogai 《Annals of the Institute of Statistical Mathematics》1977,29(1):235-246
S
e
andS
n
are independent central and noncentral Wishart matrices having Wishart distributionsW
p
(n
e
, Σ) andW
p
(n
h
, Σ; Ω) respectively. Asymptotic expansions are given for the distributions of latent roots ofS
h
S
e
−1
and of certain test statistics in MANOVA under the assumption thatn=n
e
+n
h
becomes large with a fixed ration
e
∶n
h
=e∶h(e+h=1,e>0,h>0) andΩ=O(n). 相似文献
19.
Richard A. Alò Andrè de Korvin Charles Roberts 《Annali di Matematica Pura ed Applicata》1977,112(1):33-48
Summary Under study is the existence of averaging operators determined by measurable maps φ from a measure space (S, Σ, μ) into an
arbitrary Hausdorff topological space T. The map φ induces a continuous map φe from the space Cb(T) into the normed (Banach) function space Lϱ = Lϱ(S, Σ, μ) defined by φe(f)=foφ for all f ε Cb(T). An integral representation for such operators is first studied. The existence is then determined by the existence of
an averaging operator U1 for the restriction of φ to a certain measurable subset B1 of S. Utilizing a representation of Lϱ(S, Σ, μ) as a Banach function space over a compact extremally disconnected Hausdorff space Ŝ, we are able to give a definition
for the concept of plural points and irreducible map. A significant upper bound is given for the operator U1. Finally conditions are considered under which no bounded projection from Lϱ onto the range of φe may exist. From a topological point of view the development is pursued in a general setting. Averaging operators have recently
been used for the study of injective Banach spaces of the type Cb(T) and in non-linear prediction and approximation theory relative to Tshebyshev subspaces of Lϱ.
Entrata in Redazione l’ll settembre 1975. 相似文献
20.
The singular integral operator J Ω,α, and the Marcinkiewicz integral operator (~μ)Ω,α are studied. The kernels of the operators behave like |y|-n-α(α>0) near the origin, and contain an oscillating factor ei|y|-β(β>0) and a distribution Ω on the unit sphere Sn-1 It is proved that, if Ω is in the Hardy space Hr (Sn-1) with 0<r= (n-1)/(n-1 )(>0), and satisfies certain cancellation condition,then J Ω,α and uΩ,α extend the bounded operator from Sobolev space Lpγ to Lebesgue space Lp for some p. The result improves and extends some known results. 相似文献
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