共查询到20条相似文献,搜索用时 46 毫秒
1.
Wojciech Jaworski 《Journal d'Analyse Mathématique》1998,74(1):235-273
We prove that, given an arbitrary spread out probability measure μ on an almost connected locally compact second countable
groupG, there exists a homogeneous spaceG/H, called the μ-boundary, such that the space of bounded μ-harmonic functions can be identified withL
∞
(G/H). The μ-boundary is an amenable contractive homogeneous space. We also establish that the canonical projection onto the μ-boundary
of the right random walk of law μ always converges in probability and, whenG is amenable, it converges almost surely. The μ-boundary can be characterised as the largest homogeneous space among those
homogeneous spaces in which the canonical projection of the random walk converges in probability. 相似文献
2.
Piotr Zakrzewski 《Israel Journal of Mathematics》1993,83(3):275-287
SupposeG is a group of measurable transformations of aσ-finite measure space (X, A, m). The main result of this paper gives necessary and sufficient conditions for the existence of aG-invariant,σ-finite measure defined onA and dominating the measurem in the sense of absolute continuity.
An example is also given of aσ-finite nonatomic measure space (X, A, m) together with a countable groupG of its measurable transformations such that noG-invariant,σ-finite nonatomic measure exists onA. Whether the Lebesgue space ([0, 1],L, λ) provides such an example, depends on set-theoretic assumptions.
This paper was written while the author was visiting the Technische Universitat Berlin as a research fellow of the Alexander
von Humboldt Foundation. 相似文献
3.
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional.
One of the main results in Theorem 2 which states that for a locally compact groupG, G is compact if there exists a measure μ in Soc(L
1(G)) such that μ(G) ≠ 0. We also prove thatG is finite if Soc(M(G)) is closed and every nonzero left ideal inM(G) contains a minimal left ideal. 相似文献
4.
Barak Weiss 《Israel Journal of Mathematics》1998,106(1):189-207
LetH be an ℝ-subgroup of a ℚ-algebraic groupG. We study the connection between the dynamics of the subgroup action ofH onG/G
ℤ and the representation-theoretic properties ofH being observable and epimorphic inG. We show that ifH is a ℚ-subgroup thenH is observable inG if and only if a certainH orbit is closed inG/G
ℤ; that ifH is epimorphic inG then the action ofH onG/G
ℤ is minimal, and that the converse holds whenH is a ℚ-subgroup ofG; and that ifH is a ℚ-subgroup ofG then the closure of the orbit underH of the identity coset image inG/G
ℤ is the orbit of the same point under the observable envelope ofH inG. Thus in subgroup actions on homogeneous spaces, closures of ‘rational orbits’ (orbits in which everything which can be defined
over ℚ, is defined over ℚ) are always submanifolds. 相似文献
5.
ZhaoHaixing LiuRuying ZhangShenggui 《高校应用数学学报(英文版)》2004,19(1):116-124
For a graph G,P(G,λ)denotes the chromatic polynomial of G. Two graphs G and H are said to be chromatically equivalent,denoted by G-H,if P(G,λ)=p(H,λ). Let[G]= {H|H-G}. If [G]={G},then G is said to be chromatically unique. For a complete 5-partite graph G with 5n vertices, define θ(G)=(a(G,6)-2^n 1-2^n-1 5)/2n-2,where a(G,6) denotes the number of 6-independent partitions of G. In this paper, the authors show that θ(G)≥0 and determine all graphs with θ(G)= 0, 1, 2, 5/2, 7/2, 4, 17/4. By using these results the chromaticity of 5-partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is investigated,where S is a set of edges of G. Many new chromatically unique 5-partite graphs are obtained. 相似文献
6.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 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.
Helge Glöckner 《Mathematische Zeitschrift》2008,260(4):889-904
Let G be a Lie group over a local field of characteristic p > 0 which admits a contractive automorphism α : G → G (i.e., α
n
(x) → 1 as n → ∞, for each x ∈ G). We show that G is a torsion group of finite exponent and nilpotent. We also obtain results concerning the interplay between contractive
automorphisms of Lie groups over local fields, contractive automorphisms of their Lie algebras, and positive gradations thereon.
Some of the results extend to Lie groups over arbitrary complete ultrametric fields.
Supported by the German Research Foundation (DFG), grants GL 357/2-1 and GL 357/6-1. 相似文献
9.
Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()α≤≤ ()
n
−ω. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour
number μ(G) of G: n− (n−ω)()
n
−ω≤μ(G)≤n−α() α.
Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002 相似文献
10.
V. M. Kopytov 《Algebra and Logic》2009,48(5):344-356
We create a method which allows an arbitrary group G with an infrainvariant system ℒ(G) of subgroups to be embedded in a group G* with an infrainvariant system ℒ(G*) of subgroups, so that G
α* ∩G ∈ ℒ(G) for every subgroup G
α* ∩G ∈ ℒ(G*) and each factor B/A of a jump of subgroups in ℒ(G*) is isomorphic to a factor of a jump in ℒ(G), or to any specified group H. Using this method, we state new results on right-ordered groups. In particular, it is proved that every Conrad right-ordered
group is embedded with preservation of order in a Conrad right-ordered group of Hahn type (i.e., a right-ordered group whose
factors of jumps of convex subgroups are order isomorphic to the additive group ℝ); every right-ordered Smirnov group is embedded
in a right-ordered Smirnov group of Hahn type; a new proof is given for the Holland–McCleary theorem on embedding every linearly
ordered group in a linearly ordered group of Hahn type. 相似文献
11.
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
12.
We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair
of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H
α⋈β
G ≅H
α′⋈β′
(G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then any σ-invariant isomorphism H
α⋈β
G ≅ H
α′⋈β′
G′ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications
two Schreier type classification theorems for bicrossed products of groups are given. 相似文献
13.
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
14.
Let H\G be a causal symmetric space sitting inside its complexification H
ℂ\G
ℂ. Then there exist certain G-invariant Stein subdomains Ξ of H
ℂ\G
ℂ. The Haar measure on H
ℂ\G
ℂ gives rise to a G-invariant measure on Ξ. With respect to this measure one can define the Bergman space B
2(Ξ) of square integrable holomorphic functions on Ξ. The group G acts unitarily on the Hilbert space B
2(Ξ) by left translations in the arguments. The main result of this paper is the Plancherel Theorem for B
2(Ξ), i.e., the disintegration formula for the left regular representation into irreducibles.
Received: Received: 23 November 1998 相似文献
15.
Mycielski introduced a new graph transformation μ(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-κ (resp. super edge connected or super-λ), if every minimum vertex cut (resp. minimum edge cut) isolates a vertex of G. In this paper, we show that for a connected graph G with |V(G)| ≥ 2, μ(G) is super-κ if and only if δ(G) < 2κ(G), and μ(G) is super-λ if and only if
G\ncong K2{G\ncong K_2}. 相似文献
16.
If G is a p-solvable finite group with a p-complement H and φ ∈ IBr(G), then P. Fong showed that there exists α ∈ Irr(H) such that αG=Φφ. In this note we prove that α can be chosen such that the field of values index
divides φ (1)p.
Received: 6 May 2005 相似文献
17.
Baruch Solel 《Israel Journal of Mathematics》1988,62(1):63-89
LetM be a σ-finite von Neumann algebra andα be an action ofR onM. LetH
∞(α) be the associated analytic subalgebra; i.e.H
∞(α)={X ∈M: sp∞(X) [0, ∞]}. We prove that every σ-weakly closed subalgebra ofM that containsH
∞(α) isH
∞(γ) for some actionγ ofR onM. Also we show that (assumingZ(M)∩M
α = Ci)H
∞(α) is a maximal σ-weakly closed subalgebra ofM if and only if eitherH
∞(α)={A ∈M: (I−F)xF=0} for some projectionF ∈M, or sp(α)=Γ(α). 相似文献
18.
In this paper, we consider two approaches toward the definition of a topological prime radical of a topological group. In
the first approach, the prime quasi-radical η(G) is defined as the intersection of all closed prime normal subgroups of a topological group G. Its properties are investigated. In the second approach, we consider the set η′(G) of all topologically strictly Engel elements of a topological group G. Its properties are investigated. It is proved that η′(G) is a radical in the class of all topological groups possessing a basis of neighborhoods of the identity element consisting
of normal subgroups.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 15–22, 2004. 相似文献
19.
Laurent Miclo 《Probability Theory and Related Fields》1999,114(4):431-485
Let G be a finite and connected graph, we will note by l(G) the maximum length of an injective path in G. We will show (by two dictinct proofs, one using sub-trees of G and the other based on multiflows of paths) that sup
(P,μ)∈?(G)
I(P, μ)/λ(P, μ) = l(G), where the supremum is taken over all Markovian kernels P reversible with respect to a probability μ and whose allowed transitions are given by the edges of G, and where I(P, μ) (respectively λ(P, μ)) is the isoperimetric constant (resp. the spectral gap) associated to the couple (P, μ). Then we will study more precisely the same supremum, but where the probability μ is also fixed. These results give optimal
minorations of the spectral gap which are linear with respect to the isoperimetric constant (and not quadratic, as in the
Cheeger inequality), and we will give several examples on infinite graphs.
Re?u: 12 ao?t 1997 / Version révisée: 9 novembre 1998 相似文献
20.
Hung P. Tong-Viet 《Algebras and Representation Theory》2012,15(2):379-389
Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G) be the set of all irreducible complex character degrees of G forgetting multiplicities, that is, cd(G) = {χ(1) : χ ∈ Irr(G)} and let cd
*(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be an alternating group of degree at least 5, a sporadic simple group or the Tits group. In this paper, we will show that
if G is a non-abelian simple group and cd(G) í cd(H)cd(G)\subseteq cd(H) then G must be isomorphic to H. As a consequence, we show that if G is a finite group with cd*(G) í cd*(H)cd^*(G)\subseteq cd^*(H) then G is isomorphic to H. This gives a positive answer to Question 11.8 (a) in (Unsolved problems in group theory: the Kourovka notebook, 16th edn) for alternating groups, sporadic simple groups or
the Tits group. 相似文献