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1.
A. Leibman 《Israel Journal of Mathematics》2002,129(1):29-60
A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsD
h
,h ∈G, defined byD
h
ϕ(g)=ϕ(g)
−1
ϕ(gh). We study polynomial mappings of groups, mainly to nilpotent groups. In particular, we prove that polynomial mappings to
a nilpotent group form a group with respect to the elementwise multiplication, and that any polynomial mappingG→F to a nilpotent groupF splits into a homomorphismG→G’ to a nilpotent groupG’ and a polynomial mappingG’→F. We apply the obtained results to prove the existence of the compact/weak mixing decomposition of a Hilbert space under a
unitary polynomial action of a finitely generated nilpotent group.
This work was supported by NSF, Grants DMS-9706057 and 0070566. 相似文献
2.
Mohamed Ali Toumi 《Czechoslovak Mathematical Journal》2010,60(1):85-94
Let A and B be two Archimedean vector lattices and let (A′)′
n
and (B′)′
n
be their order continuous order biduals. If Ψ: A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ***: (A′)′
n
× (A′)′
n
→ (B′)′
n
of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f-algebras. 相似文献
3.
Mohamed Krir 《manuscripta mathematica》1998,96(1):9-16
Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A
K
→B
K
→C
K
→ 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B
k
0 of the special fibre B
k
of B is a torus and we study the defect of exactmess at B in this last sequence.
Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997 相似文献
4.
Y. Félix 《Commentarii Mathematici Helvetici》1990,65(1):615-622
Denote by ζ :F →E→pB a nilpotent fibration whereF is a 1-connected space of finite category andB a finite c.w. complex with non trivial rational cohomology. In this note we compute the rational category of the space Γ* of continuous pointed sections of ζ.
Chercheur qualifié FNRS. 相似文献
5.
Let F′,F be any two closed orientable surfaces of genus g′ > g≥ 1, and f:F→ F be any pseudo-Anosov map. Then we can “extend” f to be a pseudo- Anosov map f′:F′→ F′ so that there is a fiber preserving degree one map M(F′,f′)→ M(F,f) between the hyperbolic surface bundles. Moreover the extension f′ can be chosen so that the surface bundles M(F′,f′) and M(F,f) have the same first Betti numbers.
Y. Ni is partially supported by a Centennial fellowship of the Graduate School at Princeton University. S.C. Wang is partially
supported by MSTC 相似文献
6.
M. Abad J. P. Díaz Varela B. F. López Martinolich M. del C. Vannicola M. Zander 《Central European Journal of Mathematics》2006,4(4):547-561
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L
p,k, and the finite field F(p
k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L
p,k) generated by L
p,k into the variety V(F(p
k)) generated by F(p
k) and an interpretation Φ2 of V(F(p
k)) into V(L
p,k) such that Φ2Φ1(B) = B for every B ε V(L
p,k) and Φ1Φ2(R) = R for every R ε V(F(p
k)). 相似文献
7.
L. Yu. Glebskii 《Mathematical Notes》1999,65(1):31-40
Theorems are proved establishing a relationship between the spectra of the linear operators of the formA+Ωg
iBigi
−1 andA+B
i, whereg
i∈G, andG is a group acting by linear isometric operators. It is assumed that the closed operatorsA andB
i possess the following property: ‖B
iA−1gBjA−1‖→0 asd(e,g)→∞. Hered is a left-invariant metric onG ande is the unit ofG. Moreover, the operatorA is invariant with respect to the action of the groupG. These theorems are applied to the proof of the existence of multicontour solutions of dynamical systems on lattices.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 37–47, January, 1999. 相似文献
8.
David Westreich 《Israel Journal of Mathematics》1973,16(3):279-286
Using results in bifurcation theory, we show the existence of periodic solutions of a large class of non-Lagrangian systems
of the formu″+A
1
v′+B
1u+F1
(w, w′, w″)=0v″+A
2
u′+B
2v+F2
(w, w′, w″)=0 wherew=(u, v). 相似文献
9.
We consider the differential operators Ψ
k
, defined by Ψ1(y) =y and Ψ
k+1(y)=yΨ
k
y+d/dz(Ψ
k
(y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ
k
F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z
2+β
z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ
k
(F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ
k
(f
′/f) =f
(k)/f, we deduce in particular that iff andf
(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f
′/f :f ∈F} is normal.
The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999,
and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank
Günter Frank for helpful discussions. 相似文献
10.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
11.
Mark Pankov 《Journal of Algebraic Combinatorics》2007,26(2):143-159
Let V and V′ be 2n-dimensional vector spaces over fields F and F′. Let also Ω: V× V→ F and Ω′: V′× V′→ F′ be non-degenerate symplectic forms. Denote by Π and Π′ the associated (2n−1)-dimensional projective spaces. The sets of k-dimensional totally isotropic subspaces of Π and Π′ will be denoted by and ${\mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect and by so-called base subsets. We show that every mapping of to sending base subsets to base subsets is induced by a symplectic embedding of Π to Π′. 相似文献
12.
Let F
k
be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F
k
to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F
k
→ Aut(X) corresponds to a free action of F
k
on a simplicial tree X, in particular, where φ corresponds to the action of F
k
on its Cayley graph via an automorphism of F
k
. In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F
k
). We also prove that the set of all λ(φ), where φ varies over Aut(F
k
), has a gap between 1 and 1+(2k−3)/(2k
2−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ).
The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115. 相似文献
13.
Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire
daE→B, una funzione continuaE
∞→B∞, conE
∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per
recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli
spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli.
In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche
alla classificazione delleF-fibrazioni numerabili.
Conferenza tenuta da R. Piccinini il 15 maggio 1995 相似文献
Conferenza tenuta da R. Piccinini il 15 maggio 1995 相似文献
14.
It is proved that ifE is a separable Banach lattice withE′ weakly sequentially complete,F is a Banach space andT:E→F is a bounded linear operator withT′F′ non-separable, then there is a subspaceG ofE, isomorphic toC(Δ), such thatT
G is an isomorphism, whereC(Δ) denotes the space of continuous real valued functions on the Cantor discontinuum. This generalizes an earlier result of
the second-named author. A number of conditions are proved equivalent for a Banach latticeE to contain a subspace order isomorphic toC(Δ). Among them are the following:L
1 is lattice isomorphic to a sublattice ofE′;C(Δ)′ is lattice isomorphic to a sublattice ofE′; E contains an order bounded sequence with no weak Cauchy subsequence;E has a separable closed sublatticeF such thatF′ does not have a weak order unit.
The research of both authors was partially supported by the National Science Foundation, NSF Grant No MPS 71-02839 A04. 相似文献
15.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
16.
David Mejzler 《Israel Journal of Mathematics》1987,57(1):1-27
LetX
1, ...,X
n be independent random variables, letF
i be the distribution function ofX
i (1≦i≦n) and letX
1n
≦... ≦X
nn be the corresponding order statistics. We consider the statisticsX
kn, wherek=k(n),k/n → 1 andn−k → ∞. Under some additional restrictions concerning the behaviour of the sequences {a
n>0,b
n,k(n),F
n} we characterize the class of all distribution functionsH such that Prob{(X
kn
−b
n
)/a
n
<x)}→H.
Dedicated to the Memory of N. V. Smirnov (1900–1966) 相似文献
17.
Vladimir G. Berkovich 《Israel Journal of Mathematics》1995,92(1-3):45-59
Let ϕ:Y →X be a morphism of finite type between schemes of locally finite type over a non-Archimedean fieldk, and letF be an étale constructible sheaf onY. In [Ber2] we proved that if the torsion orders ofF are prime to the characteristic of the residue field ofk then the canonical homomorphisms (R
Q
ϱ*F)an →R
q
ϱ
*
an
F
an are isomorphisms. In this paper we extend the above result to the class of sheavesF with torsion orders prime to the characteristic ofk. 相似文献
18.
A. Račkauskas 《Lithuanian Mathematical Journal》1997,37(4):402-415
Let (ξ
k
,F
k
) be a martingale difference sequence. The paper concerns the tail behavior of the quadratic formS
n
= ∑
k=1
n
∑
j=1
k−1
β
n
k−j
χ
k
χ
j
, where β
n
asn→∞. The main conclusions aboutP}n
−1
S
n
>x
n
}, wherex
n
→∞, asn→∞, are obtained using the tail behavior of a martingale with values in a certain Hilbert space.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 37, No. 4, pp. 532–549, October–December, 1997. 相似文献
19.
Michel Schreiber 《Israel Journal of Mathematics》1977,28(4):287-312
The “convex derived set” of a symmetric probability lawF on the real line is defined as the set of limits of laws ∗
j−1/k
n
F(t
j
n
η), inf 1≤j≤k
n t
j
n
→∞ ifn→∞ and the stable laws it contains are exhibited. A new criterion of stochastic compacity of the set of the powers of a probability
law is established. Finally, an isomorphism theorem between somel
p andL
0 spaces is given.
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
20.
Akito Nomura 《manuscripta mathematica》1993,79(1):379-390
LetL/k be a finite Galois extension with Galois groupG, and
a group extension. We study the existence of the Galois extensionM/L/k such that the canonical projection Gal(M/k)→Gal(L/k) coincides with the given homomorphismj:E→G and thatM/L is unramified. 相似文献