共查询到20条相似文献,搜索用时 62 毫秒
1.
J. Lindenstrauss proves in [L] thatc
0(Γ) is not quasicomplemented inl
∞(Γ) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable,
are quasicomplemented inl
∞(Γ). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace,
without isomorphic copies ofl
1 and whose dual balls are weak* sequentially compact, is quasicomplemented or not inl
∞(Γ). Especially spaces isomorphic tol
p(Γ), for 1<p<∞, have no quasicomplements inl
∞(Γ) if Γ is uncountable. 相似文献
2.
It is proved that for any Fuchsian group Γ such that ℍ/Γ is a hyperbolic Riemann surface, the Teichmüller curve V(Γ) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Γ) onto V(Γ) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmüller curves is deduced, which generalizes
a classical result that the Teichmüller curve V(Γ) depends only on the type of Γ and not on the orders of the elliptic elements of Γ when ℍ/Γ is a compact hyperbolic Riemann
surface. 相似文献
3.
Robert Schneider 《Israel Journal of Mathematics》1968,6(3):223-232
LetG be a locally compact abelian group and Γ its dual group. For any closedH ⊆G denote the algebra of restrictions toH of Fourier transforms of functions inL
1(Γ) byA(H). This paper considers certain Cantor like sets inR and ΠZ
m(j) and gives some necessary algebraic criterion fornatural isomorphisms of their restriction algebras.
This work was supported mainly by the U.S. National Science Foundation Graduate Fellowship Program.
The author wishes to thank Paul Cohen, Karel de Leeuw, and Yitzhak Katznelson for their counsel. 相似文献
4.
Tatsuya Kawabe 《manuscripta mathematica》1998,95(1):529-543
The fundamental groupΓ of a compact complete affine manifold is represented as an affine crystallographic subgroup of Aff(n). L.S.Auslander conjectured thatΓ is virtually solvable. Our purpose is to find the algebraic condition onΓ which leads affirmative answer to the conjecture. 相似文献
5.
Yves Benoist 《Inventiones Mathematicae》2006,164(2):249-278
Divisible convex sets IV: Boundary structure in dimension 3
Let Ω be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Γ of projective transformations preserving Ω such that the quotient
M := Γ\Ω is compact. We study the structure of M and of ∂Ω, when Ω is not strictly convex:
The union of the properly embedded triangles in Ω projects in M onto an union of finitely many disjoint tori and Klein bottles which induces an atoroidal decomposition of M.
Every non extremal point of ∂Ω is on an edge of a unique properly embedded triangle in Ω and the set of vertices of these
triangles is dense in the boundary of Ω (see Figs. 1 to 4).
Moreover, we construct examples of such divisible convex open sets Ω.
相似文献
6.
Marshall A. Whittlesey 《Arkiv f?r Matematik》1999,37(2):409-423
Let Δ be the closed unit disk in C, let Γ be the circle, let Π: Δ×C→Δ be projection, and letA(Δ) be the algebra of complex functions continuous on Δ and analytic in int Δ. LetK be a compact set in C2 such that Π(K)=Γ, and letK
λ≠{w∈C|(λ,w)∈K}. Suppose further that (a) for every λ∈Γ,K
λ is the union of two nonempty disjoint connected compact sets with connected complement, (b) there exists a function Q(λ,w)≠(w-R(λ))2-S(λ) quadratic in w withR,S∈A(Δ) such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ intK
λ, whereS has only one zero in int Δ, counting multiplicity, and (c) for every λ∈Γ, the map ω→Q(λ,ω) is injective on each component
ofK
λ. Then we prove that К/K is the union of analytic disks 2-sheeted over int Δ, where К is the polynomial convex hull ofK. Furthermore, we show that БК/K is the disjoint union of such disks. 相似文献
7.
Let R be a commutative ring with identity and denote Γ(R) for its zero-divisor graph. In this paper, we study the minimal embedding of the line graph associated to Γ(R), denoted by L(Γ(R)), into compact surfaces (orientable or non-orientable) and completely classify all finite commutative rings R such that the line graphs associated to their zero-divisor graphs have genera or crosscaps up to two. 相似文献
8.
LetG be a unimodular Lie group, Γ a co-compact discrete subgroup ofG and ‘a’ a semisimple element ofG. LetT
a be the mapgΓ →ag Γ:G/Γ →G/Γ. The following statements are pairwise equivalent: (1) (T
a, G/Γ,θ) is weak-mixing. (2) (T
a, G/Γ) is topologically weak-mixing. (3) (G
u, G/Γ) is uniquely ergodic. (4) (G
u, G/Γ,θ) is ergodic. (5) (G
u, G/Γ) is point transitive. (6) (G
u, G/Γ) is minimal. If in additionG is semisimple with finite center and no compact factors, then the statement “(T
a, G/Γ,θ) is ergodic” may be added to the above list.
The authors were partially supported by NSF grant MCS 75-05250. 相似文献
9.
Qi Lin Yang 《数学学报(英文版)》2008,24(4):555-564
Let a connected compact Lie group G act on a connected symplectic orbifold of orbifold fundamental group Г. If the action preserves the symplectic structure and there is a G-equivariant and mod-Г proper momentum map for the lifted action on the universal branch covering orbifold, and if the lifted G-action commutes with that of Г, then the symplectic convexity theorem is still true for this kind of lifted Hamiltonian action. 相似文献
10.
The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmüller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation Γ→G we explicitly construct open subsets of compact G-spaces, on which Γ acts properly discontinuously and with compact quotient. 相似文献
11.
This paper considers the existence of nondiscrete embeddings Γ ↦ G, where Γ is an abstract limit group and G is topological group. Namely, it is shown that a locally compact group G that admits a nondiscrete nonabelian free subgroup F admits a nondiscrete copy of every nonabelian limit group L. In some cases, for instance if the F is of rank 2 and its closure in G is compact or semisimple algebraic, or if L is a surface group (as considered in [6]), L can be chosen with the same closure as F. 相似文献
12.
13.
We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves Γ. We prove generic
injectivity and a stability estimate under the condition that the conormal bundle of Γ covers T
*
M.
Second author was partly supported by NSF Grant DMS-0400869; third author was partly supported by NSF and a Walker Family
Endowed Professorship. 相似文献
14.
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
15.
Asymptotic Geometry and Growth of Conjugacy Classes of Nonpositively Curved Manifolds 总被引:1,自引:0,他引:1
Gabriele Link 《Annals of Global Analysis and Geometry》2007,31(1):37-57
Let X be a Hadamard manifold and Γ⊂Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior
of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics
in not necessarily compact or finite volume manifolds.
Mathematics Subject Classifications (2000): 20E45, 53C22, 37F35 相似文献
16.
We prove that a function f holomorphic in a simply connected domain Ω whose Taylor series at ξ ∈ Ω is universal with respect to overconvergence automatically has a strong kind of universality: its expansion in Faber
series corresponding to any connected compact set Γ ⊂ Ω with
connected is universal, and we may take a supremum over all such Γ’s in a compact set. The topology used here is the Carathéodory
topology. This answers a question of Mayenberger and Müller.
This research is co-funded by the European Social Fund and National Resources-(EPEAEK II) PYTHAGORASII. 相似文献
17.
F. Cagnetti M. G. Mora M. Morini 《Calculus of Variations and Partial Differential Equations》2008,33(1):37-74
A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is
expressed in terms of a sign condition for a nonlocal quadratic form on H
1
0(Γ), Γ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided:
one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of Γ. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization
of the domains where the second variation is nonnegative can be given. 相似文献
18.
Jan Mayer 《manuscripta mathematica》2002,107(2):229-249
Let C
g,n
be a compact surface of genus g having n punctures, T
g,n
the associated Teichmüller space, and Γ
g,n
the corresponding Teichmüller modular group. We will show that for any subgroup Γ≤Γ
g,n
, Γ
T
g,n
≔ T
g,n
/Γ is a moduli space of curves having Γ-structure. Furthermore, we will investigate for which Γ≤Γ
g,n
and for which finite coverings P : C
g′,n′
→C
g,n
there exists a holomorphic map Φ
P
: Γ
T
g,n
→ Γ′T
g′,n′
such that for any R ? Γ
T
g,n
, Φ
P
(R) → R is topologically equivalent to P.
Received: 14 May 2001 / Revised version: 2 November 2001 相似文献
19.
Karen D. Aucoin 《Semigroup Forum》1996,52(1):157-162
A topological semigroupS is said to have thecongruence extension property (CEP) provided that for each closed subsemigroupT ofS and each closed congruence σ onT, σ can be extended to a closed congruence
onS. (That is,
∩(T xT=σ). The main result of this paper gives a characteriation of Γ-compact commutative archimedean semigroups with the congruence
extension property (CEP). Consideration of this result was motivated by the problem of characterizing compact commutative
semigroups with CEP as follows. It is well known that every commutative semigroup can be expressed as a semilattice of archimedean
components each of which contains at most one idempotemt. The components of a compact commutative semigroup need not be compact
(nor Γ-compact) as the congruence providing the decomposition is not necessarily closed. However, any component with CEP which
is Γ-compact is characterized by the afore-mentioned result. Characterization of components of a compact commutative semigroup
having CEP is a natural step towar characterization of the entire semigroup since CEP is a hereditary property. Other results
prevented in this paper give a characterization of compact monothetic semigroups with CEP and show that Rees quotients of
compact semigroups with CEP retain CEP. 相似文献
20.
Ludwig Balke 《Annals of Combinatorics》1997,1(1):297-311
A tilingT is a disordered realization of a periodic tilingP with symmetry group Γ if we can map the complement of a compact set ofT onto the quotientP/Γ in such a way that this map respects the features of the tilingT andP. We show that the global type of a 2-dimensional tilingT is determined by the periodic tilingP it is a disordered realization of, a conjugacy class of Γ which can be associated toT and a winding number. In some cases, we need in addition some kind of orientation. For higher-dimensional tilings of spaces
which are simply connected at infinity, e.g. ℝ
n
withn≥3, the associated periodic tiling alone is sufficient. 相似文献