Universality Limits, Orthogonal Polynomials and Weighted Polynomial Approximation

普适性极限、正交多项式和加权多项式近似

• 批准号: 0700427
• 负责人: Doron Lubinsky
• 金额: $ 18.9万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-15 至 2011-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700427&HistoricalAwards=false
• 关键词: Universality; Limits; Orthogonal; Polynomials; Weighted

We have developed a new approach to proving universality limits involving orthogonal polynomials. We allow, for example, the weight to be positive a.e. globally, and continuous at a given point. That is enough for universality for a fixed weight. We intend to explore the limits of this method for weights on compact and non-compact sets, as well as for varying weights.Universality limits of this type arise in the theory of random matrices and its applications, which include various topics in mathematical physics. The significance is that previously strong global hypotheses were required, such as analyticity. Now only weak local and global assumptions are required.

我们已经开发了一种新的方法来证明涉及正交多项式的普遍性限制。例如，我们允许权重为正a.e.。全局的，在给定点连续的。对于一个固定的重量来说，这就足够了。我们打算探讨这种方法的限制紧集和非紧集上的重量，以及为不同的weights.Universality这种类型的限制出现在随机矩阵理论及其应用，其中包括各种主题的数学物理。重要的是，以前强有力的全球性假设是必需的，如分析性。现在只需要弱的局部和全局假设。