共查询到20条相似文献,搜索用时 578 毫秒
1.
For a trigonometric series
defined on [−π, π)
m
, where V is a certain polyhedron in R
m
, we prove that
if the coefficients a
k
satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008. 相似文献
2.
V. V. Zhuk 《Journal of Mathematical Sciences》2009,157(4):592-606
Let
be the Fejér kernel, C be the space of contiuous 2π-periodic functions f with the norm
, let
be the Jackson polynomials of the function f, and let
be the Fejér sums of f. The paper presents upper bounds for certain quantities like
which are exact in order for every function f ∈ C. Special attention is paid to the constants occurring in the inequalities obtained. Bibliography: 14 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 90–114. 相似文献
3.
Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 < λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
4.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
moreover, for
it is impossible to decrease the constants on
. Here,
are some explicitly constructed constants,
is the modulus of continuity of order r for the function f, and
are explicitly constructed linear operators with the values in the space of periodic splines of degree
of minimal defect with 2n equidistant interpolation points. This assertion implies the sharp Jackson-type inequality
. Bibliography: 17 titles. 相似文献
5.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
相似文献
6.
We give criteria for a sequence (X
n
) of i.i.d.r.v.'s to satisfy the a.s. central limit theorem, i.e.,
相似文献
7.
Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
8.
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,
9.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
10.
O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1749-1755
Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2, ℤ) and let
11.
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square
conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues
of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion
along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization
of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square
RH-conservative) be such that
12.
V. V. Vysotsky 《Journal of Mathematical Sciences》2007,147(4):6873-6883
Let Si be a random walk with standard exponential increments. The sum ∑
i=1
k
Si is called the k-step area of the walk. The random variable
∑
i=1
k
Si plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of
this variable and prove that
13.
Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP(max 1≤k≤n|Tnk|〉εBn)〈∞ and ∞∑n=1 CnP(max 0≤k≤mn|Snk|〉εDn)〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented. 相似文献
14.
Zhang Lixin 《数学学报(英文版)》1998,14(1):113-124
Let {X, X
n
;n>-1} be a sequence of i.i.d.r.v.s withEX=0 andEX
2=σ2(0 < σ < ∞).
we obtain some sufficient and necessary conditions for
15.
István Berkes 《Probability Theory and Related Fields》1995,102(1):1-17
We give necessary and sufficient criteria for a sequence (X
n) of i.i.d. r.v.'s to satisfy the a.s. central limit theorem, i.e.,
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