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1.
Let Mn denote the maximum of a random sample of size n and Kn(a) be the number of near maxima, i.e. the number of sample observations in the fixed-width window (Mn – a, Mn]. There is a known integral criterion for almost sure convergence (to unity) of Kn(a), and we establish a similar criterion for complete convergence. We obtain simple but quite general sufficient conditions on the survivor function for satisfying the integral criteria. Further insight is obtained by seeking the rate at which P(Kn(a > 1)) tends to zero.AMS 2000 Subject Classification. 62G30, 60F15 相似文献
2.
In the present paper we prove a Korovkin type approximation theorem for a sequence of positive linear operators acting from
a weighted space Cρ1 into a weighted space Bρ2 with the use of a matrix summability method which includes both convergence and almost convergence. We also study the rates
of convergence of these operators. 相似文献
3.
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from H K αq ,p ( w1 ; w2 ) into Kαq ,p (w 1; w2). 相似文献
4.
Let 0<a<1/2,Ta,2(x)=ax and T0,2(x)=ax+1-a, and let Ka be a unique nomepty compact subset of R satisfying Ka=Ta,1(Ka)∪Ta,2(Ka). If 1/4<a<1/2, then the Hausdorff measure of Ka×Ka is strictly less than 2 - loga 22^{ - log_a 2} . If0<a≤1/4, then the Hausdorff measure of Ka×Ka is equal to 2 - loga 22^{ - log_a 2} . 相似文献
5.
De-Jun Feng 《Advances in Mathematics》2011,226(3):2470
Let π:X→Y be a factor map, where (X,σX) and (Y,σY) are subshifts over finite alphabets. Assume that X satisfies weak specification. Let a=(a1,a2)∈R2 with a1>0 and a2?0. Let f be a continuous function on X with sufficient regularity (Hölder continuity, for instance). We show that there is a unique shift invariant measure μ on X that maximizes . In particular, taking f≡0 we see that there is a unique invariant measure μ on X that maximizes the weighted entropy a1hμ(σX)+a2hμ°π−1(σY), which answers an open question raised by Gatzouras and Peres (1996) in [15]. An extension is given to high dimensional cases. As an application, we show that for each compact invariant set K on the k-torus under a diagonal endomorphism, if the symbolic coding of K satisfies weak specification, then there is a unique invariant measure μ supported on K so that dimHμ=dimHK. 相似文献
6.
In this paper we study the rates of A-statistical convergence of sequences of positive linear operators mapping the weighted space Cρ1 into the weighted space Bρ2. 相似文献
7.
In this note we study the k-hyponormality and the subnormality of Aluthge transforms of weighted shifts. It is shown that Aluthge transforms of weighted
shifts need not preserve the k-hyponormality. Moreover, we show that if W
α
is a subnormal weighted shift with 2-atomic Berger measure then its Aluthge transform [(W)\tilde]a{\widetilde{W}_\alpha} is subnormal if and only if at least one of two atoms is zero. 相似文献
8.
9.
For a family of weight functionsh
K invariant under a finite reflection group onR
d, analysis related to the Dunkl transform is carried out for the weightedL
p spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the
inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a maximal
function and use it to prove the almost everywhere convergence.
ST wishes to thank YX for the warm hospitality during his stay in Eugene. The work of YX was supported in part by the National
Science Foundation under Grant DMS-0201669. 相似文献
10.
We prove that for every polynomial-like holomorphic mapP, ifaεK (filled-in Julia set) and the componentK
aofK containinga is either a point ora is accessible along a continuous curve from the complement ofK andK
ais eventually periodic, thena is accessible along an external ray. Ifa is a repelling or parabolic periodic point, then the set of arguments of the external rays converging toa is a nonempty closed “rotation set”, finite (ifK
ais not a one point) or Cantor minimal containing a pair of arguments of external rays of a critical point in ℂ. In the Appendix
we discuss constructions via cutting and glueing, fromP to its external map with a “hedgehog”, and backward.
Partially supported by the Edmund Landau Center for Research in Mathematical Analysis, sponsored by the Minerva Foundation
(Germany).
Supported by the Polish KBN Grants 210469101 “Iteracje i Fraktale” and 210909101 “Uklady Dynamiczne”. 相似文献
11.
On a general quasismooth well-formed weighted hypersurface of degree Σ
i=14
a
i
in ℙ(1, a
1, a
2, a
3, a
4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.
相似文献
12.
Jos A. Adell Jesús de la Cal Ana Prez-Palomares 《Journal of Mathematical Analysis and Applications》1996,200(3):663
In this paper, we consider the double-indexed Bernstein power series operatorPa, tintroduced by Cheney and Sharma and related to the classical Laguerre polynomials. We obtain sharp estimates of the first two moments which allow us to prove that, when acting on a continuous functionf, the convergence ofPa, tftofis uniform on the whole interval [0, 1]. Moreover, we show that the rates of convergence depend on the way in whicht/agoes to 0. We also show thatPa, tpreserves monotonicity and global smoothness. Finally, we consider the monotonicity properties ofPa, twith respect to both parameters. To achieve the mentioned results, we use a probabilistic approach based on the representation of the operator in terms of a suitable multi-indexed stochastic process. The path properties and the martingale-type properties of this process are key points to give short proofs. 相似文献
13.
Let
r
K
a,b
be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph
r
K
a,b
to be arbitrarily decomposable into open trails. We extend the results obtained by Balister for complete graphs (Balister
in Probab Comput 10:463–499, 2001). Moreover we show that a multigraph
r
K
a,b
with even r and a ≥ 3 or b ≥ 3 is arbitrarily decomposable into open and closed trails. 相似文献
14.
We study the upper-lower class behavior of weighted sums ∑
k=1
n
a
k
X
k
, where X
k
are i.i.d. random variables with mean 0 and variance 1. In contrast to Feller’s classical results in the case of bounded
X
j
, we show that the refined LIL behavior of such sums depends not on the growth properties of (a
n
) but on its arithmetical distribution, permitting pathological behavior even for bounded (a
n
). We prove analogous results for weighted sums of stationary martingale difference sequences. These are new even in the unweighted
case and complement the sharp results of Einmahl and Mason obtained in the bounded case. Finally, we prove a general upper-lower
class test for unbounded martingales, improving several earlier results in the literature. 相似文献
15.
In this note, we study relative (pa,pb,pa,pa−b)-relative difference sets in certain p-subgroups of SL(n,K), K=Fq, where q is a prime power. 相似文献
16.
Clayton Petsche 《Mathematische Annalen》2010,348(2):449-465
We give a criterion for the weak convergence of unit Borel measures on the N-dimensional Berkovich projective space PNK{{\bf P}^{N}_K} over a complete non-archimedean field K. As an application, we give a sufficient condition for a certain type of equidistribution on PNK{{\bf P}^{N}_K} in terms of a weak Zariski-density property on the scheme-theoretic projective space
\mathbb PN[(K)\tilde]{{\mathbb P}^N_{\tilde{K{}_{\vphantom{0}}}}} over the residue field [(K)\tilde]{\tilde{K}} . As a second application, in the case of residue characteristic zero we give an ergodic-theoretic equidistribution result
for the powers of a point a in the N-dimensional unit torus
\mathbb TNK{{\mathbb T}^N_K} over K. This is a non-archimedean analogue of a well-known result of Weyl over
\mathbb C{\mathbb C} , and its proof makes essential use of a theorem of Mordell-Lang type for
\mathbb GmN{{\mathbb G}_m^N} due to Laurent. 相似文献
17.
Summary It is shown that the convergence of limit periodic continued fractionsK(a
n
/1) with lima
n
=a can be substantially accelerated by replacing the sequence of approximations {S
n
(0)} by the sequence {S
n
(x
1)}, where
. Specific estimates of the improvement are derived. 相似文献
18.
B. Enriquez 《Selecta Mathematica, New Series》2001,7(3):321-407
To any field
\Bbb K \Bbb K of characteristic zero, we associate a set
(\mathbbK) (\mathbb{K}) and a group
G0(\Bbb K) {\cal G}_0(\Bbb K) . Elements of
(\mathbbK) (\mathbb{K}) are equivalence classes of families of Lie polynomials subject to associativity relations. Elements of
G0(\Bbb K) {\cal G}_0(\Bbb K) are universal automorphisms of the adjoint representations of Lie bialgebras over
\Bbb K \Bbb K . We construct a bijection between
(\mathbbK)×G0(\Bbb K) (\mathbb{K})\times{\cal G}_0(\Bbb K) and the set of quantization functors of Lie bialgebras over
\Bbb K \Bbb K . This construction involves the following steps.? 1) To each element v \varpi of
(\mathbbK) (\mathbb{K}) , we associate a functor
\frak a?\operatornameShv(\frak a) \frak a\mapsto\operatorname{Sh}^\varpi(\frak a) from the category of Lie algebras to that of Hopf algebras;
\operatornameShv(\frak a) \operatorname{Sh}^\varpi(\frak a) contains
U\frak a U\frak a .? 2) When
\frak a \frak a and
\frak b \frak b are Lie algebras, and
r\frak a\frak b ? \frak a?\frak b r_{\frak a\frak b} \in\frak a\otimes\frak b , we construct an element
?v (r\frak a\frak b) {\cal R}^{\varpi} (r_{\frak a\frak b}) of
\operatornameShv(\frak a)?\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak a)\otimes\operatorname{Sh}^\varpi(\frak b) satisfying quasitriangularity identities; in particular,
?v(r\frak a\frak b) {\cal R}^\varpi(r_{\frak a\frak b}) defines a Hopf algebra morphism from
\operatornameShv(\frak a)* \operatorname{Sh}^\varpi(\frak a)^* to
\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak b) .? 3) When
\frak a = \frak b \frak a = \frak b and
r\frak a ? \frak a?\frak a r_\frak a\in\frak a\otimes\frak a is a solution of CYBE, we construct a series
rv(r\frak a) \rho^\varpi(r_\frak a) such that
?v(rv(r\frak a)) {\cal R}^\varpi(\rho^\varpi(r_\frak a)) is a solution of QYBE. The expression of
rv(r\frak a) \rho^\varpi(r_\frak a) in terms of
r\frak a r_\frak a involves Lie polynomials, and we show that this expression is unique at a universal level. This step relies on vanishing
statements for cohomologies arising from universal algebras for the solutions of CYBE.? 4) We define the quantization of a
Lie bialgebra
\frak g \frak g as the image of the morphism defined by ?v(rv(r)) {\cal R}^\varpi(\rho^\varpi(r)) , where
r ? \mathfrakg ?\mathfrakg* r \in \mathfrak{g} \otimes \mathfrak{g}^* .<\P> 相似文献
19.
Nazim I. Mahmudov 《Mediterranean Journal of Mathematics》2010,7(3):297-311
In the present paper, we introduce q-parametric Szász-Mirakjan operators. We study convergence properties of these operators S
n,q
(f). We obtain inequalities for the weighted approximation error of q-Szász-Mirakjan operators. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted
moduli of continuity. We also discuss Voronovskaja-type formula for q-Szász-Mirakjan operators. 相似文献
20.
The convergence behavior of the Picard iteration Xk+1=AXk+B and the weighted case Yk=Xk/bk is investigated. It is shown that the convergence of both these iterations is related to the so-called effective spectrum of A with respect to some matrix. As an application of our convergence results we discuss the convergence behavior of a sequence of scaled triangular matrices {DNTN }. 相似文献