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1.
It is proved that an irreducible quasifinite
-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight
-module is a module of the intermediate series. For a nondegenerate additive subgroup Λ ofF
n, whereF is a field of characteristic zero, there is a simple Lie or associative algebraW(Λ,n)(1) spanned by differential operatorsuD
1
m
…D
1
m
foru ∈F[Γ] (the group algebra), andm
i≥0 with
, whereD
i are degree operators. It is also proved that an indecomposable quasifinite weightW(Λ,n)(1)-module is a module of the intermediate series if Λ is not isomorphic to ℤ.
Supported by NSF grant no. 10471091 of China and two grants “Excellent Young Teacher Program” and “Trans-Century Training
Programme Foundation for the Talents” from the Ministry of Education of China. 相似文献
2.
M. Rudelson 《Israel Journal of Mathematics》1999,111(1):143-155
Lett≥1 and letn, M be natural numbers,n<M. Leta=(a
i,j
) be ann xM matrix whose rows are orthonormal. Suppose that the ℓ2-norms of the columns ofA are uniformly bounded. Namely, for allj
Using majorizing measure estimates we prove that for every ε>0 there exists, a setI ⊃ {1,…,M} of cardinality at most
such that the matrix
, whereA
I
=(a
i,j
)
j∈I
, acts as a (1+ε)-isomorphism from ℓ
2
n
into
.
Research supported in part by a grant of the US-Israel BSF. Part of this research was performed when the author held a postdoctoral
position at MSRI. Research at MSRI was supported in part by NSF grant DMS-9022140. 相似文献
3.
Binyamin Schwarz 《Israel Journal of Mathematics》1965,3(1):29-38
Letx
1,...,x
m be points in the solid unit sphere ofE
n and letx belong to the convex hull ofx
1,...,x
m. Then
. This implies that all such products are bounded by (2/m)
m
(m −1)
m−1. Bounds are also given for other normed linear spaces. As an application a bound is obtained for |p(z
0)| where
andp′(z
0)=0. 相似文献
4.
Michel Talagrand 《Israel Journal of Mathematics》1999,111(1):275-284
Consider the discrete cube Ω={0,1}
N
, provided with the uniform probabilityP. We denote byd(x, A) the Hamming distance of a pointx of Ω and a subsetA of Ω. We define the influenceI(A) of theith coordinate onA as follows. Forx in Ω, consider the pointT
i
(x) obtained by changing the value of theith coordinate. Then
We prove that we always have
Since it is easy to see that
, this recovers the well known fact that ∫Ω
d(x, A)dP(x) is at most of order
whenP(A)≥1/2. The new information is that ∫Ω
d(x, A)dP(x) can be of order
only ifA reassembles the Hamming ball {x; ∑1≤N
x
i
≥N/2}. 相似文献
5.
LetL
n be the set of lines (no two parallel) determining ann-sided bounded faceF in the Euclidean plane. We show that the number,f(L
n), of triples fromL
n that determine a triangle containingF satisfies
and these bounds are best. This result is generalized tod-dimensional Euclidean space (without the claim that the upper bound is attainable). 相似文献
6.
We exhibit, for any integerg≥2, an infinite sequenceA ∈B
2[g] such that
. Furthermore, we obtain better estimates for small values ofg. For instance, we exhibit an infinite sequenceA ∈B
2[2] such that
Partially supported by Colciencias, Colombia and Universidad del Cauca. 相似文献
7.
Johnson William B. Lindenstrauss Joram Schechtman Gideon 《Israel Journal of Mathematics》1986,54(2):129-138
It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map
fromX intoZ so that
wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.
Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.
Supported in part by NSF MCS-8102714. 相似文献
8.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
9.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
10.
Let {X
k
,k=1,2,…} be a sequence of independent binomial variables, with
the Fourier transform of the distribution ofY. Finally denote lim [P
k
− 1/2] byδ. We haveTheorem.
Research supported by N.S.F. Grant GP-25736.
Research supported by N.S.F. Grant GP-12365. 相似文献
11.
Consider the probability spaceW={−1, 1}
n
with the uniform (=product) measure. Letf: W →R be a function. Letf=Σf
IXI be its unique expression as a multilinear polynomial whereX
I=Π
i∈I
x
i. For 1≤m≤n let
=Σ|I|=m
f
IXI. LetT
ɛ
(f)=Σf
Iɛ|I|
X
I where 0<ɛ<1 is a constant. A hypercontractive inequality, proven by Bonami and independently by Beckner, states that
This inequality has been used in several papers dealing with combinatorial and probabilistic problems. It is equivalent to
the following inequality via duality: For anyq≥2
In this paper we prove a special case with a slightly weaker constant, which is sufficient for most applications. We show
where
. Our proof uses probabilistic arguments, and a generalization of Shearer’s Entropy Lemma, which is of interest in its own
right.
Supported partially by NSF Award Abstract #0071261. 相似文献
12.
V. I. Rabanovich 《Ukrainian Mathematical Journal》1999,51(8):1282-1290
We consider aC
*-algebraA generated byk self-adjoint elements. We prove that, for
, the algebraM
n
(A) is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property thatM
n
(A) is singly generated implies the relation
.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51,
No. 8, pp. 1136–1141, August, 1999. 相似文献
13.
We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally
prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsE
M,L
*
[1]. We recall that two sequencesa
n,b
nare asymptotically equal, and we writea
n
≃b
n,if and only if lim
n→∞(a
n/b
n)=1.In this paper we prove that
% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all verbally primePI-algebras a theorem of A. Giambruno and M. Zaicev [9] giving the asymptotic equality
% MathType!End!2!1! between the codimensions of the matrix algebraM
k(F) and the Capelli polynomials.
The second author is partially supported by grants RFFI 04-01-00739a, E02-2.0-26. 相似文献
14.
Yongjin Song 《Israel Journal of Mathematics》1995,90(1-3):189-197
LetR* be a simplicial involutive ring. According to certain involutions onK(R*) and
ε
L
R
∗, there are 1/2-local splittings
and
. It is known [2] that
ε
L
\ga
α
R
∗, the Wall-Witt group. SupposeI→R
S is a split extension of discrete involutive rings withI
2=0, andI is a freeS-bimodule. Then we have
and
. The trace map Tr: Prim
n
∧*M(I ⊗ ℚ)→
0
ρ
n
;I ⊗ ℚ) is an isomorphism. We prove in Lemma 1 that the trace map Tr is ℤ/2-equivariant. In Theorem 2 we show that under a certain
assumption the rational relative Wall-Witt group vanishes. Theorem 2 can be extended to a more general case (Theorem 3) by
employing Goodwillie’s reduction technique [3].
This work was partially supported by KOSEF under Grant 923-0100-010-1. 相似文献
15.
Demetrio Domínguez 《Israel Journal of Mathematics》1998,107(1):253-287
In this paper we prove a finiteness theorem for the spectral sequence (E
i(∇), (d
∇)i) associated to a transitive foliation
on a compact manifoldM, and to a flat vector bundleE overM with flat connection ∇. we also compute some examples of homogeneous Lie foliations on compact connected homogeneous spaces. 相似文献
16.
We study the functionb(n, d), the maximal number of atoms defined byn d-dimensional boxes, i.e. parallelopipeds in thed-dimensional Euclidean space with sides parallel to the coordinate axes.
We characterize extremal interval families definingb(n, 1)=2n-1 atoms and we show thatb(n, 2)=2n
2-6n+7.
We prove that for everyd,
exists and
.
Moreover, we obtainb*(3)=8/9. 相似文献
17.
Let
be the Heisenberg group and μ
r
be the normalized surface measure on the sphere of radiusr in ℂ
n
. Let
. We prove an optimalL
p-boundedness result for the spherical maximal functionMf, namely we prove thatM is bounded onL
p(I
n
) if and only ifp>2n/2n−1. 相似文献
18.
Genkai Zhang 《Israel Journal of Mathematics》2000,119(1):157-185
Let
be the invariant Cauchy Riemann operator and
the corresponding invariant Laplacians on a bounded symmetric domain. We calculate the eigenvalues ofM
m
on spherical functions. In particular we prove that for a symmetric domain of rank two the operatorsM
1,M
3 generate all invariant differential operators. We also find the eigenvalues of the generators introduced by Shimura. 相似文献
19.
Paweł Hitczenko 《Israel Journal of Mathematics》1993,84(1-2):161-178
Letf
n
= Σ
k=1
n
v
k
r
k
,n=1,…, be a martingale transform of a Rademacher sequence (r
n)and let (r
n
′
) be an independent copy of (r
n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true:
In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that
for every sequence of scalars (a
n)one has
where
is theK-interpolation norm between ℓ1 and ℓ2. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence.
This research was supported in part by an NSF grant and an FRPD grant at NCSU. 相似文献
20.
Gerhard Keller 《Israel Journal of Mathematics》1994,86(1-3):301-310
We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK]
and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim
, wherec is the unique critical point ofT. 相似文献