共查询到20条相似文献,搜索用时 31 毫秒
1.
Aleksandar Ivić 《Central European Journal of Mathematics》2004,2(4):494-508
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If
with
, then we obtain
. We also show how our method of proof yields the bound
, where T
1/5+ε≤G≪T, T<t
1<...<t
R
≤2T, t
r
+1−t
r
≥5G (r=1, ..., R−1). 相似文献
2.
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
3.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
4.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
5.
For any positive real numbers A, B, and d satisfying the conditions
, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|
A
)/log
d
(2+|x|)dx < ∞ and
. 相似文献
6.
For a positive integer n and R>0, we set
. Given R>1 and n≥4 we construct a sequence of analytic perturbations (H
j
) of the completely integrable Hamiltonian
on
, with unstable orbits for which we can estimate the time of drift in the action space. These functions H
j
are analytic on a fixed complex neighborhood V of
, and setting
the time of drift of these orbits is smaller than (C(1/ɛ
j
)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface, the result is therefore almost optimal since the stability
exponent for such orbits is 1/2(n−2). An analogous result for Hamiltonian diffeomorphisms is also proved. Two main ingredients are used in order to deal with
the analytic setting: a version of Sternberg's conjugacy theorem in a neighborhood of a normally hyperbolic manifold in a
symplectic system, for which we give a complete (and seemingly new) proof; and Easton windowing method that allow us to approximately
localize the wandering orbits and estimate their speed of drift. 相似文献
7.
G. Kuba 《Archiv der Mathematik》2002,79(6):534-542
Let
(z ∈ ℝ). Further let λ denote a large real parameter. We show that for arbitrary real numbersk and α withk>=2.7013 and 0<α≦1,
相似文献
8.
The existence of the singular integral ∫K(x, y)f(y)dy associated to a Calderón-Zygmund kernel where the integral is understood
in the principal value sense TF(x)=limε→0+∫|x−y|>εK(x, y)f(y)dy has been well studied. In this paper we study the existence of the above integral in the Cesàro-α sense. More
precisely, we study the existence of
for −1<α<0 in the setting of weighted spaces. 相似文献
9.
We prove that an absolute constantc>0 exists such that
相似文献
10.
11.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
12.
We introduce the notion of a generalized interval exchange
induced by a measurable k-partition
of [0,1).
can be viewed as the corresponding restriction of a nondecreasing function
on ℝ with
. A is called λ-dense if λ(A
i
∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that
. We give necessary and sufficient conditions for this equality to hold. We show that for each integer m≥2, such that 3∤2m+1, there exist 2 and 3 non λ-dense partitions A and B of [0,1), corresponding to the interval exchanges on 2m intervals, for which
and
commute. 相似文献
13.
We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension
ofT
we only require that
hold forf
; in this case we call
a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let {
n
}
n=0
be a weight sequence and letW
denote the associated unilateral weighted shift on
. IfW
is 2-hyponormal thenW
is weakly subnormal. Moreover, there exists a partially normal extension
on
such that (i)
is hyponormal; (ii)
; and (iii)
. In particular, if is strictly increasing then
can be obtained as
14.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
15.
A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let
be a nest with infinite dimensional atoms,
be the nest algebra associated with
and
be the closure of
, then the following result is proved
16.
Thomas Bartsch Shuangjie Peng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):778-804
We study the radially symmetric Schr?dinger equation
17.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Acta Appl Math》2000,61(1-3):101-118
From the Erds–Turán theorem, it is known that if f is a continuous function on
and L
n
(f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then
Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in
and continuous on
and making use of algebraic interpolating polynomials in the roots of unity.In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on
. 相似文献
18.
Let Δn−1 denote the (n − 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of Δn−1 obtained by starting with the full 1-dimensional skeleton of Δn−1 and then adding each 2−simplex independently with probability p. Let
denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity
19.
A. Michael Alphonse 《Journal of Fourier Analysis and Applications》2000,6(4):449-456
In this paper we prove that the maximal commutator of singular integral operator [b, T]* satisfies the inequality:
20.
Dražen Adamović 《Algebras and Representation Theory》2004,7(4):457-469
Let
be the affine Lie algebra associated to the simple finite-dimensional Lie algebra
. We consider the tensor product of the loop
-module
associated to the irreducible finite-dimensional
-module V() and the irreducible highest weight
-module L
k,. Then L
k, can be viewed as an irreducible module for the vertex operator algebra M
k,0. Let A(L
k,) be the corresponding
-bimodule. We prove that if the
-module
is zero, then the
-module
is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras. 相似文献
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