共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
We study the limit behaviour ofT
k
f and of Cesaro averagesA
n
f of this sequence, whenT is order preserving and nonexpansive inL
1
+
. IfT contracts also theL
∞-norm, the sequenceT
n
f converges in distribution, andA
n
f converges weakly inL
p
(1<p<∞), and also inL
1 if the measure is finite. “Speed limit” operators are introduced to show that strong convergence ofA
n
f need not hold. The concept of convergence in distribution is extended to infinite measure spaces.
Much of this work was done during a visit of the first author at Ben Gurion University of the Negev in Beer Sheva, supported
by the Deutsche Forschungsgemeinschaft. 相似文献
3.
W. Banaszczyk 《Discrete and Computational Geometry》1995,13(1):217-231
LetL be a lattice and letU be ano-symmetric convex body inR
n
. The Minkowski functional ∥ ∥
U
ofU, the polar bodyU
0, the dual latticeL
*, the covering radius μ(L, U), and the successive minima λ
i
(L,U)i=1,...,n, are defined in the usual way. Let ℒ
n
be the family of all lattices inR
n
. Given a pairU,V of convex bodies, we define
and kh(U, V) is defined as the smallest positive numbers for which, given arbitraryL∈ℒ
n
andu∈R
n
/(L+U), somev∈L
* with ∥v∥
V
≤sd(uv, ℤ) can be found. Upper bounds for jh(U, U
0), j=k, l, m, belong to the so-called transference theorems in the geometry of numbers. The technique of Gaussian-like measures
on lattices, developed in an earlier paper [4] for euclidean balls, is applied to obtain upper bounds for jh(U, V) in the case whenU, V aren-dimensional ellipsoids, rectangular parallelepipeds, or unit balls inl
p
n
, 1≤p≤∞. The gaps between the upper bounds obtained and the known lower bounds are, roughly speaking, of order at most logn asn→∞. It is also proved that ifU is symmetric through each of the coordinate hyperplanes, then jh(U, U
0) are less thanCn logn for some numerical constantC. 相似文献
4.
Henri Moscovici 《Israel Journal of Mathematics》1973,15(3):230-236
LetG be a Lie group,H a closed subgroup,L a unitary representation ofH andU
L the corresponding induced representation onG. The main result of this paper, extending Ol’ŝanskii’s version of the Frobenius reciprocity theorem, expresses the intertwining
number ofU
L and an irreducible unitary representationV ofG in terms ofL and the restriction ofV
∞ toH. 相似文献
5.
For a domainU on a certaink-dimensional minimal submanifold ofS
n orH
n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k
k
ω
k
M (D)
k-1
≤Vol(∂D)
k
, where ω
k
is the volume of the unit ball ofR
k
. Also, we prove that ifD is any domain on a minimal surface inS
+
n
(orH
n, respectively), thenD satisfies an isoperimetric inequality2π A≤L
2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH
n, then(k−1) Vol(U)≤Vol(∂U).
Supported in part by KME and GARC 相似文献
6.
J. Bourgain 《Israel Journal of Mathematics》1988,61(1):39-72
It is shown that the set of squares {n
2|n=1, 2,…} or, more generally, sets {n
t|n=1, 2,…},t a positive integer, satisfies the pointwise ergodic theorem forL
2-functions. This gives an affirmative answer to a problem considered by A. Bellow [Be] and H. Furstenberg [Fu]. The previous
result extends to polynomial sets {p(n)|n=1, 2,…} and systems of commuting transformations. We also state density conditions for random sets of integers in order to
be “good sequences” forL
p-functions,p>1. 相似文献
7.
We discuss local solvability of operators of the form
where theV
j
are left-invariant vector fields on the Heisenberg group such that [V
j
,V
j+n
]=U for 1≤j≤n andA=(a
jk
)=A
1+iA
2 is a complex symmetric matrix satisfying the “cone condition” |A
2|≤CA
1.
The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis”
and the TMR network “Harmonic Analysis”. 相似文献
8.
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis” subsetS of a function space. Specifically, the focus is on therate at which the lowest achievable error can be reduced as larger subsets ofS are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron,
including, in particular, a computationally attractive incremental approximation scheme. Bounds are derived for broad classes
of Banach spaces; in particular, forL
p spaces with 1<p<∞, theO (n
−1/2) bounds of Barron and Jones are recovered whenp=2.
One motivation for the questions studied here arises from the area of “artificial neural networks,” where the problem can
be stated in terms of the growth in the number of “neurons” (the elements ofS) needed in order to achieve a desired error rate. The focus on non-Hilbert spaces is due to the desire to understand approximation
in the more “robust” (resistant to exemplar noise)L
p, 1 ≤p<2, norms.
The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of
stochastic processes on function spaces. 相似文献
9.
Kok Onn Ng 《manuscripta mathematica》1995,88(1):87-107
LetU, V andW be three dimensional vector spaces over ∉ (or an alebraically closed field with characteristic not equal to 2 or 3). We prove
that the moduli space of trilinear forms onU
* ⊗V
* ⊗W
* is isomorphic to ℙ2 by applying Geometric Invariant Theory to the action ofPGL(U)×PGL(V)×PGL(W) on ℙU⊗V⊗W). 相似文献
10.
Whenϕ is an analytic map of the unit diskU into itself, andX is a Banach space of analytic functions onU, define the composition operatorC
ϕ
byC
ϕ
(f)=f o ϕ, forf∈X. In this paper we show how to use the Calderón theory of complex interpolation to obtain information on the spectrum ofC
ϕ
(under suitable hypotheses onϕ) acting on the Bloch spaceB and BMOA, the space of analytic functions in BMO. To do this we first obtain some results on the essential spectral radius
and spectrum ofC
ϕ
on the Bergman spacesA
pand Hardy spacesH
p,spaces which are connected toB and BMOA by the interpolation relationships [A
1,B]
t
=A
pand [H
1,BMOA]
t
=H
pfor 1=p(1−t). 相似文献
11.
Miran Cerne 《Journal d'Analyse Mathématique》1997,72(1):261-278
Letp be an analytic disc attached to a generating CR-submanifoldM of C
n
. It is proved that some recently introduced conditions onp andM which imply that the family of all smallC
α
holomorphic perturbations ofp alongM is a Banach submanifold of (Aα(D))n are equivalent. These conditions are given in terms of the partial indices of the discp attached toM and “holomorphic sections” of the conormal bundle ofM along p(∂D). Also, a sufficient geometric conditionon p andM is given so that the family of all smallC
α
holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (A
α
(D))n. 相似文献
12.
Heinrich Steinlein 《manuscripta mathematica》1996,89(1):15-33
Summary LetK be a compact space andf:K→K a continuous map without fixed points, i.e. Fixf=⊘. For prime numbersp, the sets Fixf
p are freeℤ/p-spaces with theℤ/p-action induced byf. Our aim is to estimate the topological indicesi(F
p,f) of invariant subsetsF
p⊂Fixf
p approximating a givenS⊂K.
We construct an example (K,f,S) withS⊂Fixf
q (q being some prime number) such that, for each neighborhoodU ofS, i (Fix (f|u)
p, f) increases linearly withp.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
13.
LetF be a field of characteristicp. Teichmüller proved that anyp-algebra overF of indexp
n
and exponentp
e
is similar to a tensor product with at mostp
n
!(p
n
!−1) factors of cyclicp-algebras overF of degreep
e
. In this note we improve Teichmüller bound for two particular types ofp-algebras. LetL be a finite separable extension ofF. IfA is a cyclicp-algebra overL of degreep
e
we show that Cor
L/F
A, the corestriction ofA, is similar to a tensor product with at most [L :F] factors of cyclicp-algebras overF of degreep
e
. Moreover we prove that [L :F] is the best possible bound. From this we deduce that ifA is a cyclicp-algebra overF of degreep
n
and exponentp
e
thenA is similar to a tensor product with at mostp
n−e
factors of cyclicp-algebras overF of degreep
e
. 相似文献
14.
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
15.
William A. Veech 《Journal d'Analyse Mathématique》1990,55(1):117-171
The cotangent bundle ofJ (g, n) is a union of complex analytic subvarieties, V(π), the level sets of the function “singularity pattern” of quadratic differentials.
Each V(π) is endowed with a natural affine complex structure and volume element. The latter contracts to a real analytic volume
element, Μπ, on the unit hypersurface, V1(π), for the Teichmüller metric. Μπ is invariant under the pure mapping class group, γ(g, n), and a certain class of functions is proved to be Lp(Μπ), 0 <p < 1, over the moduli space V1(π)/γ (g, n). In particular, Μπ(V1(π)/γ(g, n)) < ∞, a statement which generalizes a theorem by H. Masur.
Research supported by NSF-MCS-8219148 and NSF-DMS-8521620. 相似文献
16.
A code D over Z
2
n
is called a quasi-perfect Lee distance-(2t + 1) code if d
L(V,W) ≥ 2t + 1 for every two code words V,W in D, and every word in Z
2
n
is at distance ≤ t + 1 from at least one code word, where D
L(V,W) is the Lee distance of V and W. In this paper we present a fast decoding algorithm for quasi-perfect Lee codes. The basic idea of the algorithm comes from
a geometric representation of D in the 2-dimensional plane. It turns out that to decode a word it suffices to calculate its distance to at most four code
words. 相似文献
17.
Huang Cheng-gui 《数学学报(英文版)》1992,8(3):225-235
SupposeX and the coefficientsA
1, …,A
m aren×n matrices. LetB be anmn×mn matrix as in (7). LetJ be the Jordan canonical matrix ofB andB=PJP
−. LetE
i denote thei×i unit matrix.V is defined bydV/dt=JV andV(t=0)=E
mn. ThenZ=PV satisfiesdZ/dt=BZ.P
* is a matrix which consists of the firstn rows ofP. The author proves: There is a solution of (1) ↔ there are anmn×n matrixC, ann×n matrixQ and ann×n function matrixN such thatP
*VC=QN, where detQ≠0 andN is defined byN(t=0)=E
n anddN/dt=RN, in whichR is ann×n Jordan canonical matrix. There are three cases regarding the solutions of (1): No solution, finitek solutions, 1<k<C
n
m
, and infinite solutions which containj parameters, 1<-j<-mn
2. 相似文献
18.
It is shown that thep-summing norm of any operator withn-dimensional domain can be well-aproximated using only “few” vectors in the definition of thep-summing norm. Except for constants independent ofn and logn factors, “few” meansn if 1<p<2 andn
p/2 if 2<p<∞.
Supported in part by NSF #DMS90-03550 and the U.S.-Israel Binational Science Foundation.
Supported in part by the U.S.-Israel Binational Science Foundation. 相似文献
19.
巫世权 《高校应用数学学报(英文版)》1993,8(2):175-181
Let Cdenote the set of all k-subests of an n-set.Assume Alohtain in Ca,and A lohtain in (A,B) is called a cross-2-intersecting family if |A B≥2 for and A∈A,B∈B.In this paper,the best upper bounds of the cardinalities for non-empty cross-2-intersecting familles of a-and b-subsets are obtained for some a and b,A new proof for a Frankl-Tokushige theorem[6] is also given. 相似文献