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1.
The authors consider the length, , of the longest increasing subsequence of a random permutation of numbers. The main result in this paper is a proof that the distribution function for , suitably centered and scaled, converges to the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest descent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel for the Poissonization of the distribution function of .

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2.
非线性灰色离散系统零解的稳定性   总被引:9,自引:1,他引:8  
本文用区间矩阵和Lyapunov第二方法讨论了具有非线性扰动项的灰色离散系统的稳定性,得到了若干稳定性的代数判据,这些结果将文(5)的主要结果由线性推广到了非线性,并给出了实现的例子。  相似文献
3.
基于Laguerre函数的Landau型不等式   总被引:6,自引:2,他引:4  
基于经典正交的广义 Laguerre多项式 Lsn( x)建立了 Landau型不等式 ,并且指出其不等式的系数在某种意义上是最好可能的 ,加强并推广了 Varma和 Bojanov的结果 .  相似文献
4.
Orthogonal polynomials for exponential weights on   总被引:4,自引:4,他引:0  
Let I=[0,d), where d is finite or infinite. Let , where and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight , obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.  相似文献
5.
带小波函数的Cauchy主值积分的数值计算   总被引:4,自引:1,他引:3  
1 引言 众所周知,小波方法在信号处理和图像处理方面发挥了举世瞩目的成就。近年来人们研究小波方法在数值分析方面的应用。期望在数值求解微分方程和积分方程方面发挥良好的作用。本文研究带有小波函数的Cauchy主值积分 的数值计算方法,其中Φ(x)是紧支撑的尺度函数。这是数值求解积分方程的核心问题之一。 1.l 多分辩分析 空间L~2(R)中的一个多分辩分析是这样的闭子空间列{V_j},它满足下列条件 1) 2) 3) 4)存在尺度函数,使构成V_o的Riesz基,从而也存在序列使满足双尺度方程  相似文献
6.
扩充的Hermite-Fejér插值算子平均收敛性   总被引:3,自引:0,他引:3       下载免费PDF全文
讨论了以Jacobi正交多项式零点为插值结点的扩充Hermite-Fejer插值算子在Lpu空间的平均收敛性。首先给出了算子加权平均收敛的条件,进一步得到了收敛阶。  相似文献
7.
Wavelets Based on Orthogonal Polynomials   总被引:2,自引:0,他引:2  
We present a unified approach for the construction of polynomial wavelets. Our main tool is orthogonal polynomials. With the help of their properties we devise schemes for the construction of time localized polynomial bases on bounded and unbounded subsets of the real line. Several examples illustrate the new approach.

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8.
扩充的Hermite—Fejer插值算子平均收敛性   总被引:2,自引:0,他引:2  
文成林  张书玲 《数学学报》1999,42(3):429-440
讨论了以Jacobi正交多项式零点为插值结点的扩充Hermite-Fejer插值算子在Lu^p空间的平均收敛性。首先给出了算子加权平均收敛的条件,进一步得到了收敛阶。  相似文献
9.
Matrix orthogonal polynomials whose derivatives are also orthogonal   总被引:2,自引:2,他引:0  
In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general sequence of matrix orthogonal polynomials, not necessarily associated with a hermitian functional. We give several examples of non-diagonalizable positive definite weight matrices satisfying a Pearson-type equation, which show that the previous results are non-trivial even in the positive definite case.A detailed analysis is made for the class of matrix functionals which satisfy a Pearson-type equation whose polynomial of degree not greater than 2 is scalar. We characterize the Pearson-type equations of this kind that yield a sequence of matrix orthogonal polynomials, and we prove that these matrix orthogonal polynomials satisfy a second order differential equation even in the non-hermitian case. Finally, we prove and improve a conjecture of Durán and Grünbaum concerning the triviality of this class in the positive definite case, while some examples show the non-triviality for hermitian functionals which are not positive definite.  相似文献
10.
The zeros of linear combinations of orthogonal polynomials   总被引:2,自引:1,他引:1  
Let {pn} be a sequence of monic polynomials with pn of degree n, that are orthogonal with respect to a suitable Borel measure on the real line. Stieltjes showed that if m<n and x1,…,xn are the zeros of pn with x1<<xn then there are m distinct intervals f the form (xj,xj+1) each containing one zero of pm. Our main theorem proves a similar result with pm replaced by some linear combinations of p1,…,pm. The interlacing of the zeros of linear combinations of two and three adjacent orthogonal polynomials is also discussed.  相似文献
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