G-Frame and Riesz Sequences in Hilbert Spaces

G-frames generalize frames in Hilbert spaces. The literatures show that g-frames and frames share many similar properties, while they behave differently in redundancy and perturbation properties. Interestingly, g-frames have been extensively studied, but g-frame sequences have not. This problem is nontrivial since a g-frame and a frame both involve all vectors in the same Hilbert space, while a g-frame sequence and a frame sequence do not. They involve different linear spans. Using the synthesis and Gram matrix methods, we in this paper characterize g-frame sequences and g-Riesz sequences; obtain the Pythagorean theorem for g-orthonormal systems. These results recover several known results and lead to some new results on g-frames.     

两两NQD列的收敛性质

本文首先给出两两 ＮＱＤ列的 Ｋｏｌｍｏｇｏｒｏｖ型不等式，进而讨论两两 ＮＱＤ列的收敛性质，获得了与独立情形一样的Ｂａｕｍ和Ｋａｔｚ完全收敛定理，几乎达到独立惰形著名的Ｍａｒｃｉｎｋｉｅｗｉｃｚ强大数定律、三级数定理等结果．     

Quasi-Regular Sequences and Regular Sequences

In this article, we give a comparison between the behavior of R-regular sequences under passage to quotient and to localization and that of R-quasi-regular sequences. On the other hand, we use these results to construct two examples of R-quasi-regular sequences which are not R-regular.     

关于迭代数列的审敛法

从迭代数列及其基本性质出发,给出单调有界定理、压缩映象原理、Cauchy收敛准则和上(下)极限四种判别迭代数列收敛的方法.     

Interpolating Sequences of Parabolic Bergman Spaces

The parabolic Bergman space is a Banach space of L ^p -solutions of some parabolic equations on the upper half-space H. We study interpolating theorem for these spaces. It is shown that if a sequence in H is δ-separated with δ sufficiently near 1, then it interpolates on parabolic Bergman spaces. This work was supported in part by Grant-in-Aid for Scientific Research (C) No.18540168, No.18540169, and No.19540193, Japan Society for the Promotion of Science.     

$\psi$混合序列的一些收敛性质

In this paper,we extend the Kolmogorov-type inequality to the case of ψ-mixing sequences.Moreover,we study the strong limit theorems for partial sums of ψ-mixing random variables.As a result,we extend the Khintchine-Kolmogorov-type convergence theorem,the three series theorem,Marcinkiewicz strong law of large number to the case of ψ-mixing sequences.     

负相关随机变量序列的对数律

在本文中,首先我们得到了负相关(ND)随机变量序列的指数不等式和矩不等式,然后运用这些不等式讨论了ND序列的对数律.结果,我们将独立情形下的对数律推广到ND序列情形下依然成立.     

凸序列不等式的控制证明

利用控制不等式理论简洁地证明了一类凸序列不等式 (包括著名的 Nanson不等式的几个推广 ) ,并给出若干应用 .     

关于~*-mixing随机变量序列的强大数定律

利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 .     

Density Modulo 1 of Sublacunary Sequences

We prove the existence of real numbers badly approximated by rational fractions whose denominators form a sublacunar sequence. For example, for the ascending sequence s _n , n = 1, 2, 3, ..., generated by the ordered numbers of the form 2ⁱ3^j, i, j = 1, 2, 3, ..., we prove that the set of real numbers α such that inf _n∈ℕ n‖s _n α‖ > 0 is a set of Hausdorff dimension 1. The divergence of the series implies that the Lebesgue measure of those numbers is zero.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 803–813.Original Russian Text Copyright ©2005 by R. K. Akhunzhanov, N. G. Moshchevitin.     

A combinatorial approach to height sequences in finite partially ordered sets

Fix an element x of a finite partially ordered set P on n elements. Then let h_i(x) be the number of linear extensions of P in which x is in position i, counting from the bottom. The sequence {h_i(x):1≤i≤n} is the height sequence of x in P. In 1982, Stanley used the Alexandrov–Fenchel inequalities for mixed volumes to prove that this sequence is log-concave, i.e., for 1≤i≤n−2. However, Stanley’s elegant proof does not seem to shed any light on the error term when the inequality is not tight; as a result, researchers have been unable to answer some challenging questions involving height sequences in posets. In this paper, we provide a purely combinatorial proof of two important special cases of Stanley’s theorem by applying Daykin’s inequality to an appropriately defined distributive lattice. As an end result, we prove a somewhat stronger result, one for which it may be possible to analyze the error terms when the log-concavity bound is not tight.     

NSD随机变量序列的完全收敛性

本文利用NSD随机变量序列的性质、矩不等式及三级数定理,在一定的矩条件下,得到了NSD随机变量序列的完全收敛性.所得结果推广了 Chow与Lai[15,16]与Jajte[17]的独立序列的结果.     

Representation Theorems for the Sequences of the Classes CRc and ERc

We prove two representation theorems in the Bojanic–Seneta sense for the classes CR _c and ER _c of O-regularly varying sequences.     

确定递推式数列收敛的几种方法

给出确定递推式数列收敛的三种方法,即利用单调有界定理、极限的精确定义以及压缩影像原理,举例说明其应用.     

两个数列极限的再推广

证明了三个命题,它们是已知的数列极限的推广.     

两个数列极限的推广

证明了四个命题 ,它们是两个已知的数列极限的推广 .     

Local Limit Theorems for Sequences of Simple Random Walks on Graphs

In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to supercritical percolation clusters, graph trees converging to the continuum random tree and the homogenisation problem for nested fractals. A subsequential local limit theorem for the simple random walks on generalised Sierpinski carpet graphs is also presented.      

Invariant Core Theorems for Double Sequences

The definition for the convergence of a double sequence was presented by A. Pringsheim [9]. Recently, the definitions of limit inferior, limit superior, and the core of a double sequence are presented. By using these definitions and the notion of regularity for four-dimensional matrices, an invariant core theorem for double sequences is presented.AMS Subject Classification (2000) primary 40B05 secondary 40C05     

Time-frequency localization for the short time Fourier transform

We use some estimating of orthogonal projection in a reproducing kernel Hilbert space, to prove a sharp quantitaive form of Shapiro's mean dispersion theroem with generalized dispersion for the short time Fourier transform. Other forms of localization of orthonormal sequences in L²?^d) notably the umbrella theorem, are also proved for the short time Fourier transform.