共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
A mapT: X→X on a normed linear space is callednonexpansive if ‖Tx-Ty‖≤‖x-y‖∀x, y∈X. Let (Ω, Σ,P) be a probability space,
an increasing chain of σ-fields spanning Σ,X a Banach space, andT: X→X. A sequence (xn) of strongly
-measurable and stronglyP-integrable functions on Ω taking on values inX is called aT-martingale if
.
LetT: H→H be a nonexpansive mapping on a Hilbert spaceH and let (xn) be aT-martingale taking on values inH. If
then x
n
/n converges a.e.
LetT: X→X be a nonexpansive mapping on ap-uniformly smooth Banach spaceX, 1<p≤2, and let (xn) be aT-martingale (taking on values inX). If
then there exists a continuous linear functionalf∈X
* of norm 1 such that
If, in addition, the spaceX is strictly convex, x
n
/n converges weakly; and if the norm ofX
* is Fréchet differentiable (away from zero), x
n
/n converges strongly.
This work was supported by National Science Foundation Grant MCS-82-02093 相似文献
3.
V. A. Kofanov 《Ukrainian Mathematical Journal》2006,58(10):1538-1551
We establish new exact Bernstein-type and Kolmogorov-type inequalities. The main result of this work is the following exact
inequality for periodic splines s of order r and defect 1 with nodes at the points iπ/n, i ∈ Z, n ∈ N:
where k, r ∈ N, k < r, p = 1 or p = 2, q > p, and ϕr is the perfect Euler spline of order r.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1357–1367, October, 2006. 相似文献
4.
Saharon Shelah 《Israel Journal of Mathematics》2008,166(1):61-96
We show that, consistently, there is an ultrafilter on ω such that if N
nℓ = (P
nℓ ∪ Q
nℓ, P
nℓ, Q
nℓ, R
nℓ) (for ℓ = 1, 2, n < ω), P
nℓ ∪ Q
nℓ ⊆ ω, and are models of the canonical theory t
ind of the strong independence property, then every isomorphism from onto is a product isomorphism.
The first version of this work done in 93; First typed: May 1993.
This research was partially supported by the United States-Israel Binational Science Foundation. Publication 509 相似文献
5.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
相似文献
6.
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
7.
De Li LI Fu Xing ZHANG Andrew ROSALSKY 《数学学报(英文版)》2007,23(3):557-562
Let {X, Xn; n≥ 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n ≥ 1} be a sequence of positive constants such that
an↑∞ and 1〈 lim inf n→∞ a2n/an≤lim sup n→∞ a2n/an〈∞
Set Sn=∑i=1^n Xi,n≥1.In this paper we prove that
∑n≥1 1/n P(||Sn||≥εan)〈∞ for all ε〉0
if and only if
lim n→∞ Sn/an=0 a.s.
This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut. 相似文献
8.
A. Koldobsky 《Israel Journal of Mathematics》1999,110(1):75-91
It is proved that for arbitrarymεℕ and for a sufficiently nontrivial compact groupG of operators acting on a “typical”n-dimensional quotientX
n
ofl
1
m
withm=(1+δ)n, there is a constantc=c(δ) such that
Supported in part by KBN grant no. 2 P03A 034 10. 相似文献
9.
Frank Blume 《Israel Journal of Mathematics》1998,108(1):1-12
If (X,T) is a completely ergodic system, then there exists a positive monotone increasing sequence {a
n
}
n
1/∞
with lim
n
→∞a
n
=∞ and a positive concave functiong defined on [1, ∞) for whichg(x)/x
2 isnot integrable such that
for all nontrivial partitions α ofX into two sets. 相似文献
10.
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
11.
Let X, X1 , X2 , . . . be i.i.d. random variables, and set Sn = X1 +···+Xn , Mn = maxk≤n |Sk|, n ≥1. Let an = o( (n)(1/2)/logn). By using the strong approximation, we prove that, if EX = 0, VarX = σ2 0 and E|X| 2+ε ∞ for some ε 0, then for any r 1, lim ε1/(r-1)(1/2) [ε-2-(r-1)]∞∑n=1 nr-2 P{Mn ≤εσ (π2n/(8log n))(1/2) + an } = 4/π . We also show that the widest a n is o( n(1/2)/logn). 相似文献
12.
There are reverse inequalities for square functions of differences arising in ergodic theory and differentiation of functions.
For example, it is shown that if An is the usual average in ergodic theory, and (nk∶k=1,2,3,...) is an increasing lacunary sequence with no non-trivial common divisor, then one has for any p, 1<p<∞, there
is a constant Cp such that for all f∃ Lp(X),
13.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
14.
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
15.
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
16.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
17.
Li Xin Zhang 《数学学报(英文版)》2008,24(4):631-646
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
18.
Zhi-Wei Sun 《Israel Journal of Mathematics》2002,128(1):135-156
In this paper we study [
r
n
]
m
=Σ
k≡r(modm) (
k
n
) wherem>0,n≥0 andr are integers. We show that [
r
n
]
m
(m>2) can be expressed in terms of some linearly recurrent sequences with orders not exceeding ϕ(m)/2. In particular, we determine [
r
n
]
12
explicitly in terms of first order and second order recurrences. It follows that for any primep>3 we have
and
.
The research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions
of MOE, and the National Natural Science Foundation of P. R. China. 相似文献
19.
J. Sivak-Fischler 《Acta Mathematica Hungarica》2007,116(4):327-375
Combining Goldston-Yildirim’s method on k-correlations of the truncated von Mangoldt function with Maier’s matrix method, we show that for all r ≧ 1 where p
n
denotes the nth prime number and γ is Euler’s constant. This is the best known result for any r ≧ 11.
相似文献
20.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
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