共查询到20条相似文献,搜索用时 31 毫秒
1.
We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups
and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G). 相似文献
2.
N. I. Zhukova 《Siberian Mathematical Journal》2011,52(3):436-450
We prove that each codimension q ≥ 3 conformal foliation (M,F) either is Riemannian or has a minimal set that is an attractor. If (M,F) is a proper conformal foliation that is not Riemannian then there exists a closed leaf that is an attractor. We do not assume
that M is compact. Moreover, if M is compact then a non-Riemannian conformal foliation (M,F) is a (Conf(S
q
), S
q
)-foliation with a finite family of attractors, and each leaf of this foliation belongs to the basin of at least one attractor. 相似文献
3.
Given a multivalued mappingF, we address the problem of finding another multivalued mappingS that agrees locally withF. We limit ourselves to the case whenF(x) is convex compact for eachx. We propose anS obtained by linearizing the support function ofF(x) and give conditions under which thisS approximatesF in the sense of Hausdorff distance. We show equality betweenS and other proposals obtained from tangent cones to the graph ofF. Finally, we apply these results to the approximate subdifferential of a convex function. 相似文献
4.
Jurek Czyzowicz Bruno Gaujal Eduardo Rivera-Campo Jorge Urrutia Joseph Zaks 《Geometriae Dedicata》1995,56(2):115-120
A setL of points in thed-spaceE
d
is said toilluminate a familyF={S
1, ...,S
n
} ofn disjoint compact sets inE
d
if for every setS
i
inF and every pointx in the boundary ofS
i
there is a pointv inL such thatv illuminatesx, i.e. the line segment joiningv tox intersects the union of the elements ofF in exactly {x}.The problem we treat is the size of a setS needed to illuminate a familyF={S
1, ...,S
n
} ofn disjoint compact sets inE
d
. We also treat the problem of putting these convex sets in mutually disjoint convex polytopes, each one having at most a certain number of facets. 相似文献
5.
Andreas Matuschke 《Mathematische Nachrichten》2000,211(1):109-126
We consider a compact twistor space P and assume that there is a surface S ⊂ P, which has degree one on twistor fibres and contains a twistor fibre F, e.g. P a LeBrun twistor space ([20], [18]). Similar to [6] and [5] we examine the restriction of an instanton bundle V equipped with a fixed trivialization along F to a framed vector bundle over (S, F). First we develope inspired by [13] a suitable deformation theory for vector bundles over an analytic space framed by a vector bundle over a subspace of arbitrary codimension. In the second section we describe the restriction as a smooth natural transformation into a fine moduli space. By considering framed U(r)‐instanton bundles as a real structure on framed instanton bundles over P, we show that the bijection between isomorphism classes of framed U(r)‐instanton bundles and isomorphism classes of framed vector bundles over (S, F) due to [5] is actually an isomorphism of moduli spaces. 相似文献
6.
We derive the integral inequality of a Randers metric with isotropic S-curvature in terms of its navigation representation. Using the obtained inequality we give some rigidity results under the condition of Ricci curvature. In particular, we show the following result: Assume that an n-dimensional compact Randers manifold (M, F) has constant S-curvature c. Then (M, F) must be Riemannian if its Ricci curvature satisfies that Ric 〈 -(n - 1)c^2. 相似文献
7.
Let S be a compact set in R
2. For S simply connected, S is a union of two starshaped sets if and only if for every F finite, F
bdry S, there exist a set G
bdry S arbitrarily close to F and points s, t depending on G such that each point of G is clearly visible via S from one of s, t. In the case where S has at most finitely many components, the necessity of the condition still holds while the sufficiency fails. 相似文献
8.
A. B. Aleksandrov 《Journal of Mathematical Sciences》2004,120(5):1645-1652
We study Toeplitz–Schur multipliers of the Schatten–von Neumann class S
p for 0 < p < 1. We describe all functions F on an arbitrary commutative locally compact group G satisfying the following condition: for any integral operator in S
p with kernel function k(x,y), the kernel function F(x-y)k(x)k(y) defines also an integral operator in S
p. Bibliography: 4 titles. 相似文献
9.
Oscar Perdomo 《Israel Journal of Mathematics》2006,156(1):65-71
Let (S
i, gi),i=1, 2 be two compact riemannian surfaces isometrically embedded in euclidean spaces. In this paper we show that ifM=S
1×S2,then for any functionF: M→R, the graph ofF, i.e. the manifold {(x, F(x)): x∈M}, does not have positive sectional curvature. 相似文献
10.
Let F be a finite field of characteristic not 2, and SF a subset with three elements. Consider the collectionThen (F,S) is a simple 2-design and the parameter λ of (F,S) is 1, 2, 3 or 6. We find in this paper the full automorphism group of (F,S). Namely, if we put U={r | {0,1,r}S} and K the subfield of F generated by U, then the automorphisms of (F,S) are the maps of the form xg(α(x))+b, xF, where bF, α : F→F is a field automorphism fixing U, and g is a linear transformation of F considered as a vector space over K. 相似文献
S={S·a+b | a,bF, a≠0}.
11.
Christiane Kraus 《Constructive Approximation》2011,33(2):191-217
The aim of this paper is to extend the classical maximal convergence theory of Bernstein and Walsh for holomorphic functions
in the complex plane to real analytic functions in ℝ
N
. In particular, we investigate the polynomial approximation behavior for functions F:L→ℂ, L={(Re z,Im z):z∈K}, of the structure F=g[`(h)]F=g\overline{h}, where g and h are holomorphic in a neighborhood of a compact set K⊂ℂ
N
. To this end the maximal convergence number ρ(S
c
,f) for continuous functions f defined on a compact set S
c
⊂ℂ
N
is connected to a maximal convergence number ρ(S
r
,F) for continuous functions F defined on a compact set S
r
⊂ℝ
N
. We prove that ρ(L,F)=min {ρ(K,h)),ρ(K,g)} for functions F=g[`(h)]F=g\overline{h} if K is either a closed Euclidean ball or a closed polydisc. Furthermore, we show that min {ρ(K,h)),ρ(K,g)}≤ρ(L,F) if K is regular in the sense of pluripotential theory and equality does not hold in general. Our results are based on the theory
of the pluricomplex Green’s function with pole at infinity and Lundin’s formula for Siciak’s extremal function Φ. A properly chosen transformation of Joukowski type plays an important role. 相似文献
12.
S. I. Maksymenko 《Ukrainian Mathematical Journal》2011,62(10):1577-1584
Let M be a smooth connected orientable compact surface and let Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) be a space of all Morse functions f : M → S
1 without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : V → S
1 is either a constant map or a covering map. The space Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) is endowed with the C
∞-topology. We present the classification of connected components of the space Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) . This result generalizes the results obtained by Matveev, Sharko, and the author for the case of Morse functions locally
constant on ∂M. 相似文献
13.
Mitsuyasu Hashimoto 《代数通讯》2013,41(4):1524-1562
Let F be an affine flat group scheme over a commutative ring R, and S an F-algebra (an R-algebra on which F acts). We define an equivariant analogue Q F (S) of the total ring of fractions Q(S) of S. It is the largest F-algebra T such that S ? T ? Q(S), and S is an F-subalgebra of T. We study some basic properties. Utilizing this machinery, we give some new criteria for factoriality (unique factorization domain property) of (semi-)invariant subrings under the action of affine algebraic groups, generalizing a result of Popov. We also prove some variations of classical results on factoriality of (semi-)invariant subrings. Some results over an algebraically closed base field are generalized to those over an arbitrary base field. 相似文献
14.
Xian Zhang 《Linear and Multilinear Algebra》2013,61(5):349-358
Suppose F is a field of characteristic not 2. Let Mn F and Sn F be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from Sn F to Sn F (respectively, Mn F) preserving Moore–Penrose inverses of matrices are characterized. We first characterize all additive Moore–Penrose inverse preserving maps from Sn F to Mn F, and thereby, all additive Moore–Penrose inverse preserving maps from Sn F to itself are characterized by restricting the range of these additive maps into the symmetric matrix space. 相似文献
15.
Marilyn Breen 《Journal of Geometry》1989,35(1-2):14-18
SetS inR
d has propertyK
2 if and only ifS is a finite union ofd-polytopes and for every finite setF in bdryS there exist points c1,c2 (depending onF) such that each point ofF is clearly visible viaS from at least one ci,i = 1,2. The following characterization theorem is established: Let
, d2. SetS is a compact union of two starshaped sets if and only if there is a sequence {S
j
} converging toS (relative to the Hausdorff metric) such that each setS
j satisfies propertyK
2. For
, the sufficiency of the condition above still holds, although the necessity fails. 相似文献
16.
A. Tiemeyer 《Transformation Groups》1997,2(2):215-223
In the preceding paper [AT] compactness propertiesC
n
andCP
n
for locally compact groups were introduced. They generalize the finiteness propertiesF
n
andFP
n
for discrete groups. In this paper a local-global principle forS-arithmetic groups over number fields is proved. TheS-arithmetic group is of typeF
n
, resp.FP
n
, if and only if for allp inS thep-adic completionG
p
of the corresponding algebraic groupG is of typeC
n
resp.CP
n
. As a corollary we obtain an easy proof of a theorem of Borel and Serre: AnS-arithmetic subgroup of a semisimple group has all the finiteness propertiesF
n
. 相似文献
17.
18.
We obtain a family of eight-dimensional unital division algebras over a field F out of a separable quadratic field extension S of F, a three-dimensional anisotropic hermitian form h over S of determinant one and an element c ∈ S
× not contained in F. These algebras are not third-power associative. 相似文献
19.
LetX be a projective scheme over a noetherian base schemeS, and letF be a coherent sheaf onX. For any coherent sheaf ε onX, consider the set-valued contravariant functor Hom(ε,F)S-schemes, defined by Hom(ε,F) (T)= Hom(ε
T
,F
T) where ε
T
andF
T are the pull-backs of ε andF toX
T =X x
S
T. A basic result of Grothendieck ([EGA], III 7.7.8, 7.7.9) says that ifF is flat over S then Komε,F) is representable for all ε.
We prove the converse of the above, in fact, we show that ifL is a relatively ample line bundle onX over S such that the functor Hom(L
-n
,F) is representable for infinitely many positive integersn, thenF is flat overS. As a corollary, takingX =S, it follows that ifF is a coherent sheaf on S then the functorT ↦H°(T, F
t) on the category ofS-schemes is representable if and only ifF is locally free onS. This answers a question posed by Angelo Vistoli.
The techniques we use involve the proof of flattening stratification, together with the methods used in proving the author’s
earlier result (see [N1]) that the automorphism group functor of a coherent sheaf onS is representable if and only if the sheaf is locally free. 相似文献
20.
LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT
5, be the translate ofT bys inS defined byT
5(x)=(Tx)
5
. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T
5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT
5. 相似文献