Mathematical Sciences: Multivariate Orthogonal Polynomials and Hypergeometric Functions of Matrix Argument

数学科学：多元正交多项式和矩阵论证的超几何函数

• 批准号: 9304290
• 负责人: Robert Gustafson
• 金额: $ 6万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304290&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariate; Orthogonal; Polynomials

This award supports the research of Professor Gustafson to work in combinatorics. Professor Gustafson will work on a class of orthogonal polynomials that were defined by Askey and Wilson. These polynomials have applications as diverse as quantum physics and additive number theory. It is proposed to explicitly construct multivariate generalizations of the Askey-Wilson polynomials expressed in terms of a new generalization of hypergeometric functions of a matrix argument. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.

该奖项支持古斯塔夫森教授在组合学方面的研究。 古斯塔夫森教授将研究由阿斯基和威尔逊定义的一类正交多项式。 这些多项式具有多种应用，例如量子物理学和加法数论。 建议显式地构造以矩阵参数的超几何函数的新泛化形式表示的 Askey-Wilson 多项式的多元泛化。 该研究属于组合学的一般领域。 组合学试图找到有效的方法来研究如何组织离散集合。 离散系统的行为对于现代通信极其重要。 例如，电话系统等大型网络的设计以及计算机科学中的算法设计都涉及离散对象，而这都利用了组合研究。