共查询到20条相似文献,搜索用时 631 毫秒
1.
Akihito Hora 《Journal of Theoretical Probability》1992,5(1):71-100
Investigated is quasi-invariance of power probabilities on the infinite product ofSU(2). We consider the subgroup consisting of those actions which keep a measure quasi-invariant (i.e., mutually absolutely continuous) and call it the quasi-invariant subgroup of the measure. We establish several estimations for the quasi-invariant subgroups in terms oflfp-type subgroups ofSU(2). Our methods are based on Hellinger integrals, Fourier analysis, and spherical functions onSU(2). 相似文献
2.
We study the structure of finite groups whosemaximal subgroups have the Hall property. We prove that such a group G has at most one non-Abelian composition factor, the solvable radical S(G) admits a Sylow series, the action of G on sections of this series is irreducible, the series is invariant with respect to this action, and the quotient group G/S(G) is either trivial or isomorphic to PSL2(7), PSL2(11), or PSL5(2). As a corollary, we show that every maximal subgroup of G is complemented. 相似文献
3.
Tomasz Weiss 《Topology and its Applications》2008,156(1):138-141
We show that it is consistent with ZFC that there exist:
- (1)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN, but without the Menger property.
- (2)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN with the Menger property which does not have the Rothberger property.
4.
Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics
The distribution μcl of a Poisson cluster process in X=Rd (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in X=n?Xn, with intensity measure defined as a convolution of the background intensity of cluster centres and the probability distribution of a generic cluster. We show that the measure μcl is quasi-invariant with respect to the group of compactly supported diffeomorphisms of X and prove an integration-by-parts formula for μcl. The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. 相似文献
5.
6.
Magnus B. Landstad 《Journal of Functional Analysis》2002,191(2):211-223
We study properties of C*-algebraic deformations of homogeneous spaces G/Γ which are equivariant in the sense that they preserve the natural action of G by left translation. The center is shown to be isomorphic to C(G/G0ρ) for a certain subgroup G0ρ of G, and there is a 1-1 correspondence between normalised traces and probability measures on G/G0ρ. This makes it possible to represent the deformed algebra as operators over L2(G/Γ). Applications to K-theory are also mentioned. 相似文献
7.
We consider functionsf(z),z∈D, of one complex variable that satisfy the following weakened asymptotic monogeny condition: for some positiveσ<1/2,f(z) is monogenic at each pointξ∈D with respect to some setG(ξ) such that the lower density ofG(ξ) atξ is greater than 1/2+σ. We show that if for somep σ ≥1 the function (log+|?(z)|) p σ is locally integrable inD with respect to the plane Lebesgue measure, thenf(z) is holomorphic inD. 相似文献
8.
Barbara Schapira 《Comptes Rendus Mathematique》2003,336(4):349-352
In this Note, we generalize a result of Goodman–Plante, who characterizes limit points of averaging sequences as holonomy invariant transverse measures. We prove an analogous result for some leafwise averages, weighted with a cocycle Δ, whose limit points are a product of a quasi-invariant transverse measure with respect to Δ with a leafwise measure. To cite this article: B. Schapira, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
9.
A. M. Vershik 《Journal of Fixed Point Theory and Applications》2008,3(2):317-329
We consider the sequence of the hyperspheres M
n
, i.e., the homogeneous transitive spaces of the Cartan subgroup of the group and study the normalized limit of the corresponding sequence of invariant measures m
n
on those spaces. In the case of compact groups and homogeneous spaces, for example, for the classical pairs (SO(n), S
n-1), n = 1, 2, … , the limit of the corresponding measures is the classical infinite-dimensional Gaussian measure; this is the well-known
Maxwell-Poincaré lemma. Simultaneously the Gaussian measure is a unique (up to a scalar) invariant measure with respect to
the action of the infinite orthogonal group O(∞). This coincidence implies the asymptotic equivalence between grand and small canonical ensembles for the series of the
pairs (SO(n), S
n-1). Our main result shows that the situation for noncompact groups, for example for the case , is completely different: the limit of the measures m
n
does not exist in the literal sense, and we show that only a normalized logarithmic limit of the Laplace transforms of those
measures does exist. At the same time, there exists a measure which is invariant with respect to a continuous analogue of
the Cartan subgroup of the group GL(∞), the so-called infinite-dimensional Lebesgue measure (see [7]). This difference is an evidence for non-equivalence between
the grand and small canonical ensembles in the noncompact case.
To my friend Dima Arnold 相似文献
10.
Kenneth D. Johnson 《Journal of Functional Analysis》1979,34(1):54-71
Let G be a linear semisimple Lie group of split rank one with K a maximal compact subgroup. In this paper, we consider the space Cc∞(G:F) of all functions in Cc∞(G) whose left and right K-translates span a finite-dimensional space. Using the analytic continuation of the principal series to define the Fourier transform, we give a characterization of the Fourier transform of the space Cc∞(G:F). This gives an analog of the classical Paley-Wiener theorem which gives a characterization of the Fourier transform of the space Cc∞(Rn). 相似文献
11.
Fang Xiaochun 《数学学报(英文版)》1998,14(4):541-546
LetG be a second countable groupoid with Haar system {λ
u
},A be an abelian group which left invariant acts onG. Then we have aC
*-dynamic system (C
*
(G, A, β). In this paper we have studied the existence of quasi-invariant measure with certain properties; using these measures some
important results about crossed products and groupoidC
*-algebras have been obtained.
This work is supported by National Natural Science Foundation of China 相似文献
12.
I. Ferrando 《Indagationes Mathematicae》2009,20(1):57-71
Let m be a countably additive vector measure with values in a real Banach space X, and let L1(m) and Lw(m) be the spaces of functions which are, correspondingly, integrable and weakly integrable with respect to m. Given a Young's function Φ, we consider the vector measure Orlicz spaces LΦ(m) and LΦw(m) and establish that the Banach space of multiplication operators going from W = LΦ(m) into Y = L1 (m) is M = LΨw (m) with an equivalent norm; here Ψ is the conjugated Young's function for Φ. We also prove that when W = LΦw(m), Y = L1(m) we have M = LΨw (m), and when W = LΦw(m), Y = L1(m) we have M = LΨ (m). 相似文献
13.
We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π+ of G how does π+ decompose on restriction to H. Here G is GL+(2,F), where F is a nonarchimedian local field of characteristic not two, K a separable quadratic extension of F, GL+(2,F) the subgroup of index 2 in GL(2,F) consisting of those matrices whose determinant is in NK/F(K∗), π+ is an irreducible, admissible supercuspidal representation of GL+(2,F) and H=K∗ under an embedding of K∗ into GL(2,F). 相似文献
14.
Let T be a free ergodic measure-preserving action of an abelian group G on (X,μ). The crossed product algebra RT=L∞(X,μ)? G has two distinguished masas, the image CT of L∞(X,μ) and the algebra ST generated by the image of G. We conjecture that conjugacy of the singular masas ST(1) and ST(2) for weakly mixing actions T(1) and T(2) of different groups implies that the groups are isomorphic and the actions are conjugate with respect to this isomorphism. Our main result supporting this conjecture is that the conclusion is true under the additional assumption that the isomorphism γ : RT(1)→RT(2) such that γ(ST(1))=ST(2) has the property that the Cartan subalgebras γ(CT(1)) and CT(2) of RT(2) are inner conjugate. We discuss a stronger conjecture about the structure of the automorphism group Aut(RT,ST), and a weaker one about entropy as a conjugacy invariant. We study also the Pukanszky and some related invariants of ST, and show that they have a simple interpretation in terms of the spectral theory of the action T. It follows that essentially all values of the Pukanszky invariant are realized by the masas ST, and there exist non-conjugate singular masas with the same Pukanszky invariant. 相似文献
15.
R. A. Wilson 《Siberian Mathematical Journal》2013,54(1):159-172
We give a construction of the compact real form of the Lie algebra of type E 6, using the finite irreducible subgroup of shape 33+3: SL3(3), which is isomorphic to a maximal subgroup of the orthogonal group Ω7(3). In particular we show that the algebra is uniquely determined by this subgroup. Conversely, we prove from first principles that the algebra satisfies the Jacobi identity, and thus give an elementary proof of existence of a Lie algebra of type E 6. The compact real form of F 4 is exhibited as a subalgebra. 相似文献
16.
Ali Ghaffari 《Czechoslovak Mathematical Journal》2012,62(3):729-742
Let G be a locally compact group. We continue our work [A. Ghaffari: Γ-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ-amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G. In this paper, among other things, we introduce and study a closed subspace A Γ p (G) of L ∞(Γ) and then characterize the Γ-amenability of G using A Γ p (G). Various necessary and sufficient conditions are found for a locally compact group to possess a Γ-invariant mean. 相似文献
17.
Yoshinobu Kamishima 《Topology and its Applications》1985,19(2):189-199
This note will concern properly discontinuous actions of subgroups in real algebraic groups on contractible manifolds. Let (π,X,ρ) be such an action, where ρ:π→ Diff(X) is a homomorphism. We assume that ? extends to a smooth action of a real algebraic group G containing π. If such π has a nontrivial radical (i.e., unique maximal normal solvable subgroup), then we can apply the method of Seifert construction [14],[17] to yield that the quotient π\X supports the structure of an injective Seifert fibering with typical (resp. exceptional) fiber diffeomorphic to a solv (resp. infrasolv)-manifold (when π acts freely). When G is an amenable algebraic group, we can say about a uniqueness property for such actions. Namely, let (πi, Xi, ρi) be actions as above (i= 1,2). Then, given an isomorphism f of π1 onto ?2, there is a diffeomorphism h: X1→X2 such that h(ρ1(r)x)=ρ2(f(r)h(x).As an application, we try to decide the structure of affine motions of some euclidean space n. First we verify the conjecture of [17, 4 5], i.e., a compact complete affinely flat manifold admits a maximal toral action if its fundamental group has a nontrivial center. Second, a compact complete affinity flat manifold whose fundamental group is virtually polycyclic supports the structure of an infrasolvmanifold. This structure varies depending on its solvable kernel (if it is abelian or nilpotent, it must be a euclidean space form or an infranilmanifold respectively). If a group of the affine group A(n) acts properly discontinuously and with compact quotient of n, then it is called an affine crystallographic group. Finally, we can say so far as to a uniqueness property that two virtually polycyclic affine crystallographic groups are conjugate inside Diff(n) if they are isomorphic (cf.[8]). 相似文献
18.
We study the first cohomology groups of a countable discrete group G with coefficients in a G-module ?Φ(G), where Φ is an N-function of class Δ2(0) ∩ ?2(0). Developing the ideas of Puls and Martin-Valette for a finitely generated group G, we introduce the discrete Φ-Laplacian and prove a theorem on the decomposition of the space of Φ-Dirichlet finite functions into the direct sum of the spaces of Φ-harmonic functions and ?Φ(G) (with an appropriate factorization). We prove also that if a finitely generated group G has a finitely generated infinite amenable subgroup with infinite centralizer then \(\bar H^1\) (G, ?Φ(G)) = 0. In conclusion, we show the triviality of the first cohomology group for the wreath product of two groups one of which is nonamenable. 相似文献
19.
Ramesh Gangolli 《Journal of Functional Analysis》1977,25(3):244-252
Let G be a locally compact motion group, i.e., it is a semidirect product of a compact subgroup with a closed abelian normal subgroup, the action of the compact subgroup on the other one being by conjugation. The main result of this paper is that the group algebra of such a group is symmetric. This result is then used to prove that a generalization of the Wiener-Tauberian theorem holds for such groups. Precisely, it is shown that every proper closed two-sided ideal in L1(G) is annihilated by an irreducible unitary representation of G, lifted to L1(G). 相似文献
20.
Xicheng Zhang 《Stochastic Processes and their Applications》2011,121(6):1373-1388
In this article we prove that stochastic differential equation (SDE) with Sobolev drift on a compact Riemannian manifold admits a unique ν-almost everywhere stochastic invertible flow, where ν is the Riemannian measure, which is quasi-invariant with respect to ν. In particular, we extend the well-known DiPerna-Lions flows of ODEs to SDEs on a Riemannian manifold. 相似文献