共查询到20条相似文献,搜索用时 687 毫秒
1.
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
2.
Let II be a bounded symmetric domain, ω ⇉ I a bounded subdomain, and let
denote the weighted Bergman space of holomorphic square integrable functions on I. Let Tλ, ω be the Berezin-Toeplitz operator on
with symbol χΩ and kth eigenvalue λ
k
(T
λ,Ω). We prove that for δ1 sufficiently close to 0 and δ2 sufficiently close to 1 the estimate
holds for all domains ω satisfying the condition |{z ∈ I |d(z, Ω) < ε}| ≤c|Ω|, where d is the invariant distance on I and |ω| is the invariant volume of ω. The proof is based on the fact that the
operator norm of the Berezin transform is smaller than 1. Our main technical tool are some of the formulae for the Berezin
transform obtained by Unterberger and Upmeier in [11]. 相似文献
3.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
4.
Let {Xk} be a sequence of i.i.d. random variables with d.f. F(x). In the first part of the paper the weak convergence of the d.f.'s
Fn(x) of sums
is studied, where 0<α≤2, ank>0, 1≤k≤mn, and, as n→∞, bothmax
1≤k≤mna
nk→0 and
. It is shown that such convergence, with suitably chosen An's and necessarily stable limit laws, holds for all such arrays {αnk} provided it holds for the special case αnk=1/n, 1≤k≤n. Necessary and sufficient conditions for such convergence are classical. Conditions are given for the convergence
of the moments of the sequence {Fn(x)}, as well as for its convergence in mean. The second part of the paper deals with the almost sure convergence of sums
, where an≠0, bn>0, andmax
1≤k≤n ak/bn→0. The strong law is said to hold if there are constants An for which Sn→0 almost surely. Let N(0)=0 and N(x) equal the number of n≥1 for which bn/|an|<x if x>0. The main result is as follows. If the strong law holds,EN (|X1|)<∞. If
for some 0<p≤2, then the strong law holds with
if 1≤p≤2 and An=0 if 0<p<1. This extends the results of Heyde and of Jamison, Orey, and Pruitt. The strong law is shown to hold under various
conditions imposed on F(x), the coefficients an and bn, and the function N(x).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
5.
Victor I. Lomonosov Heydar Radjavi Vladimir G. Troitsky 《Integral Equations and Operator Theory》2008,60(3):405-418
An algebra of operators on a Banach space X is said to be transitive if X has no nontrivial closed subspaces invariant under every member of the algebra. In this paper we investigate a number of
conditions which guarantee that a transitive algebra of operators is “large” in various senses. Among these are the conditions
of algebras being localizing or sesquitransitive. An algebra is localizing if there exists a closed ball B ∌ 0 such that for every sequence (x
n
) in B there exists a subsequence and a bounded sequence (A
k
) in the algebra such that converges to a non-zero vector. An algebra is sesquitransitive if for every non-zero z ∈ X there exists C > 0 such that for every x linearly independent of z, for every non-zero y ∈ X, and every there exists A in the algebra such that and ||Az|| ≤ C||z||. We give an algebraic version of this definition as well, and extend Jacobson’s density theorem to algebraically sesquitransitive
rings.
The second and the third authors were supported by NSERC. 相似文献
6.
7.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
8.
Zbigniew Slodkowski 《Journal of Geometric Analysis》1997,7(4):637-651
We consider an arbitrary real analytic family Xz,
, over the closed unit disc
, of real analytic plane Jordan curves Xz. Ifj
e
iθ
,e
iθ
∋ ∂D, is an arbitrary real-analytic family of orientation-reversing homeomorphisms of
fixingX
e
iθ
pointwise, we show that there is a unique holomorphic motion of
extending the given motion of Jordan curves and consistent with the given family of involutions. If these generalized reflections
are defined using the barycentric extension construction of Douady-Earle-Nag, then the resulting extension method for holomorphic
motions of X is natural, that is Moebius-invariant and continuous with respect to variation of the given motion of X0. 相似文献
9.
We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space WN,2([0, ∞); e−x) and the Sobolev-Legendre space WN,2([−1, 1]) with respect to the Sobolev-Laguerre inner product
and with respect to the Sobolev-Legendre inner product
respectively, where a0 = 1, ak ≥0, 1 ≤k ≤N −1, γ > 0, and N ≥1 is an integer. 相似文献
10.
L. Brandolini G. Gigante A. Greenleaf A. Iosevich A. Seeger G. Travaglini 《Journal of Geometric Analysis》2007,17(1):15-40
We consider Fourier transforms
of densities supported on curves in ℝd. We obtain sharp lower and close to sharp upper bounds for the decay rates of
as R → ∞. 相似文献
11.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):115-120
Let
be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel
P(β) of all power series
such that
. We give a necessary and sufficient condition for a polynomial to be cyclic inl
P(β) and a point to be bounded point evaluation onl
P(β). 相似文献
12.
Oscar Blasco 《Arkiv f?r Matematik》2000,38(1):21-36
Inequalities of the form
for allf∈H
1, where {m
k
} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy's inequality
and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms ff atoms and that they
actually characterizeB-convexity. It is also shown that for 1<q<∞ and 0<α<∞ the spaceX=H(1,q,γa) consisting of analytic functions on the unit disc such that
satisfies the previous inequality for vector valued functions inH
1 (X), defined as the space ofX-valued Bochner integrable functions on the torus whose negative Fourier coefficients vanish, for the case {m
k
}={2k} but not for {m
k
}={k
a
} for any α ∈ N.
The author has been partially supported by the Spanish DGICYT, Proyecto PB95-0291. 相似文献
13.
A. V. Ustinov 《Journal of Mathematical Sciences》2006,137(2):4722-4738
Statistical properties of continued fractions for numbers a/b, where a and b lie in the sector a, b ≥ 1, a2 + b2 ≤ R2, are studied. The main result is an asymptotic formula with two meaning terms for the quantity
where sx(a/b) = |{j ε {1, …, s}: [0; tj, …, ts] ≤ x}| is the Gaussian statistic for the fraction a/b = [t0; t1, …, ts]. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 186–211. 相似文献
14.
A. I. Nazarov 《Journal of Mathematical Sciences》2000,101(2):2975-2986
In the case 1≤p<q≤∞, the question on the exact constant in the embedding of the space W
p
1
(0,1) into the space Lq(0,1) is studied, i.e.,
where the norm is defined by the equality
. Bibliography: 5 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 149–163. 相似文献
15.
Ilya V. Boikov 《分析论及其应用》1996,12(3):59-67
Local splines are presented for the approximation of functions of one and many variables, which are analytic in the domains
, where Ui(zi) is a unit disk in the complex plane Ci,i=1,2,…,l, l=1,2, …. Results are given for functions whose r-order derivatives belong to the Hardy's class Hp,1≤p≤∞. It is shown that the approximation converge to the function at the rate
for functions of one variable and An−(r−1/p)/(l−1) for functions of l variables, where n is the number of points of local splines and A and C are positive constants.
This work was supported by Russian Foundation of Fundumental Inverstigations 相似文献
16.
Vidmantas Bentkus 《Israel Journal of Mathematics》2007,158(1):1-17
Let M
n
= X
1 + ⋯ + X
n
be a martingale with bounded differences X
m
= M
m
− M
m
−1 such that ℙ{a
m
− σ
m
≤ X
m
≤ a
m
+ σ
m
} = 1 with nonrandom nonnegative σ
m
and σ(X
1, …, X
m
−1)-measurable random variables a
m
. Write σ
2 = σ
1
2
+ ⋯ + σ
n
2
. Let I(x) = 1 − Φ(x), where Φ is the standard normal distribution function. We prove the inequalities
with a constant c such that 3.74 … ≤ c ≤ 7.83 …. The result yields sharp bounds in some models related to the measure concentration. In the case where all a
m
= 0 (or a
m
≤ 0), the bounds for constants improve to 3.17 … ≤ c ≤ 4.003 …. The inequalities are new even for independent X
1, …, X
n
, as well as for linear combinations of independent Rademacher random variables.
Research supported by Max Planck Institute for Mathematics, Bonn 相似文献
17.
Boris Rubin 《Journal of Fourier Analysis and Applications》2000,6(2):185-205
Approximate and explicit inversion formulas are obtained for a new class of exponential k-plane transforms defined by
where x∈ℝn, Θ is a k-frame in ℝn, 1≤k≤n−1, μ∈ℂk is an arbitrary complex vector. The case k=1, μ∈ℝ corresponds to the exponential X-ray transform arising in single photon
emission tomography. Similar inversion formulas are established for the accompanying transform
where V is a real (n×k)-matrix. Two alternative methods, leading to the relevant continuous wavelet transforms, are presented.
The first one is based on the use of the generalized Calderón reproducing formula and multidimensional fractional integrals
with a Bessel function in the kernel. The second method employs interrelation between Pμ and the associated oscillatory potentials. 相似文献
18.
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X
1,X
2, … is any sequence of integrable i.i.d. random variables, then
$
\mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }}
{{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.
$
\mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }}
{{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.
相似文献
19.
We construct integral operators Rr and Hr on a regular q-pseudoconcave CR manifoldM such that
20.
Pu Zhang 《数学学报(英文版)》2008,24(8):1387-1400
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,
||μ(f)||LP(ω)≤C|Mf|LP(ω) and ||μb(f)||LP(ω)≤C||ML(log L)^1/r f||LP(ω). The weighted weak L(log L)^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献 |