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21.
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
22.
A. M. Vinogradov 《Acta Appl Math》1989,15(1-2):3-21
The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. 相似文献
23.
Saida Sultanic 《Integral Equations and Operator Theory》2006,55(4):573-595
The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman
space La2. We also analyze the analogous problem for weighted Bergman spaces La,α2, − 1 < α < ∞. 相似文献
24.
采用基于第一原理的全势能线性缀加平面波加局域轨道((L)APW lo)方法对Nd(Fe,Si)11Cx化合物(x=0,2)的电子结构进行了计算,得到了化合物态密度和磁矩等信息.计算结果表明NdFe9Si2化合物中Si原子主要与4b和32i位Fe原子产生杂化,导致Fe原子磁矩减小.NdFe9Si2C2化合物C原子使32i位Fe原子磁矩进一步降低,同时减弱了Si原子的影响,使得4b位Fe原子磁矩增大. 相似文献
25.
26.
Khaled Al-Takhman 《Journal of Pure and Applied Algebra》2002,173(3):245-271
In this article we defined and studied quasi-finite comodules, the cohom functors for coalgebras over rings. Linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing but a cotensor functor. Our main result of this work characterizes equivalences between comodule categories generalizing the Morita-Takeuchi theory to coalgebras over rings. Morita-Takeuchi contexts in our setting is defined and investigated, a correspondence between strict Morita-Takeuchi contexts and equivalences of comodule categories over the involved coalgebras is obtained. Finally, we proved that for coalgebras over QF-rings Takeuchi's representation of the cohom functor is also valid. 相似文献
27.
Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given. 相似文献
28.
本文首先将文[1]中的BLD映射推广为弱(L1,L2)-BLD映射,并证明了如下正则性结果:存在两个可积指数 P1=P1(n,L1,L2)<n<q1=q1(n,L1,L2),使得对任意弱(L1,L2)-BLD映射f∈(Ω,Rn),都有f∈(Ω,Rn),即f为(L1,L2)-BLD映射. 相似文献
29.
Kunyu Guo 《Journal of Functional Analysis》2004,213(2):380-411
This paper mainly concerns defect operators and defect functions of Hardy submodules, Bergman submodules over the unit ball, and Hardy submodules over the polydisk. The defect operator (function) carries key information about operator theory (function theory) and structure of analytic submodules. The problem when a submodule has finite defect is attacked for both Hardy submodules and Bergman submodules. Our interest will be in submodules generated by polynomials. The reason for choosing such submodules is to understand the interaction of operator theory, function theory and algebraic geometry. 相似文献
30.
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities
related to the multisection of formal power series with noncommutative coefficients.
Received November 19, 2004 相似文献