共查询到20条相似文献,搜索用时 13 毫秒
1.
Isometric Group Actions on Hilbert Spaces: Growth of Cocycles 总被引:1,自引:0,他引:1
Yves de Cornulier Romain Tessera Alain Valette 《Geometric And Functional Analysis》2007,17(3):770-792
We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence
of 1-cocycles with linear growth, we obtain the following alternative for a class of amenable groups G containing polycyclic groups and connected amenable Lie groups: either G has no quasi-isometric embedding into a Hilbert space, or G admits a proper cocompact action on some Euclidean space.
On the other hand, noting that almost coboundaries (i.e. 1-cocycles approximable by bounded 1-cocycles) have sublinear growth,
we discuss the converse, which turns out to hold for amenable groups with “controlled” F?lner sequences; for general amenable
groups we prove the weaker result that 1-cocycles with sufficiently small growth are almost coboundaries. Besides, we show
that there exist, on a-T-menable groups, proper cocycles with arbitrary small growth.
Received: August 2005 Revision: October 2006 Accepted: November 2006 相似文献
2.
Herbert Abels 《Geometriae Dedicata》2001,87(1-3):309-333
In this survey article we discuss the structure of properly discontinuous groups of affine transformations and in particular of affine crystallographic groups. One of the main open questions is Auslander's conjecture claiming that every affine crystallographic group is virtually solvable. 相似文献
3.
4.
We consider the complexes of Hilbert spaces whose differentials are closed densely-defined operators. A peculiarity of these complexes is that from their differentials we can construct Laplace operators in every dimension. The Laplace operator together with a sufficiently nice measurable function enables us to define a generalized Sobolev space. There exist pairs of measurable functions allowing us to construct some canonical mappings of the corresponding Sobolev spaces. We find necessary and sufficient conditions for those mappings to be compact. In some cases for a given Hilbert complex we can construct an associated Sobolev complex. We show that the differentials of the original complex are normally solvable simultaneously with the differentials of the associated complex and that the reduced cohomologies of these complexes coincide. 相似文献
5.
Potential Analysis - In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear... 相似文献
6.
Karin Melnick 《Geometriae Dedicata》2007,126(1):131-154
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general
construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group
is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the
assumption they are real-analytic. 相似文献
7.
In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and order α, almost starlikeness of order α, spirallikeness of type of β and starlikeness. 相似文献
8.
Anis Rezgui 《Acta Appl Math》2005,89(1-3):271-286
In this work we study partial differential operators of infinite order on spaces of entire functions, generalizing some of
the results presented in [2] and [5] to the new spaces introduced in [3]. 相似文献
9.
V. Paulsen and D. Singh gave a characterization of certain Hilbertspaces contractively contained in Lp, p 2. Here, the analogof their theorem is proved for 1 p < 2. 2000 MathematicsSubject Classification 47A15 (primary), 46E30 (secondary). 相似文献
10.
Let S=G/K be a strongly irreducible, simply connected, compact symmetric space and let
be its group of isometries. We classify the symmetric spaces among these that admit free, isometric circle actions. The existence of such actions is important in constructing examples of manifolds with positive sectional curvature. 相似文献
11.
In this paper, we obtain a generalization of the method of regularizing multipliers for the solution of the Hilbert boundary-value problem with finite index in the theory of analytic functions to the case of an infinite power-behaved index. This method is used to obtain a general solution of the homogeneous Hilbert problem for the half-plane, a solution that depends on the existence and the number of entire functions possessing mirror symmetry with respect to the real axis and satisfying some additional constraints related to the singularity characteristic of the index. To solve of the inhomogeneous problem, we essentially use a specially constructed solution of the homogeneous problem whereby we reduce the boundary condition of the Hilbert problem to a Dirichlet problem. 相似文献
12.
在一般Banach空间中研究了一类无穷区间上不连续非线性积分方程的唯一解.在非常弱的条件下证明了非线性积分方程的唯一解可以由迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计式,然后应用到无穷区间一阶微分方程的终值问题,本质改进(将紧型条件删去)并推广了一些结果. 相似文献
13.
14.
15.
16.
Kai WANG 《数学年刊B辑(英文版)》2007,28(3):321-326
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd). 相似文献
17.
Our main result is that the simple Lie group G = Sp(n, 1) acts metrically properly isometrically on L
p
(G) if p > 4n + 2. To prove this, we introduce Property , with V being a Banach space: a locally compact group G has Property if every affine isometric action of G on V, such that the linear part is a C
0-representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic
groups over a local field of characteristic zero, have Property . As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on L
2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L2-Betti number is nonzero.
相似文献
18.
A Note on Certain Block Spaces on the Unit Sphere 总被引:1,自引:0,他引:1
Xiao Feng YE Xiang Rong ZHU 《数学学报(英文版)》2006,22(6):1843-1846
In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1(S^n-1)+L(ln+L)^1+v(s^n-1),v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq^0.v(S^n-1)are proper subspaces of H1 (S^n- 1), 相似文献
19.
For infinite-dimensional homotopy space forms X/G with G nontrivial finite cyclic groups, we study the homotopy type of X/G. We show that the Euler class of X/G is not zero if and only if X/G is finitely dominated. 相似文献
20.
关于Hilbert空间单位球面上等距延拓的注记 总被引:3,自引:1,他引:3
本文指出,文[1]中有关在单位球面S1[H]上的1-Lipschitz假设条件减弱为“局部1-Lipschitz”条件时,那里的等距定理仍然成立. 相似文献