Harmonic Analysis and Special Functions

谐波分析和特殊功能

• 批准号: 9703705
• 负责人: Donald Richards
• 金额: $ 9.9万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703705&HistoricalAwards=false
• 关键词: Harmonic; Analysis; Special; Functions

ABSTRACT Richards Richards will continue his program of research on hypergeometric functions defined on matrix spaces and on symmetric cones. Special attention will be paid to the theory of operator-valued hypergeometric functions on the symmetric cones. In the second part of the project the principal investigator will continue his research on applications of these special functions, and general techniques in harmonic analysis and representation theory, to the areas of multivariate statistics, total positivity, probability inequalities, and related combinatorial problems. Richards is interested in research problems Modern Analysis, a subfield of mathematics, for two reasons. First, Modern Analysis is an important branch of mathematics with fundamental links to astronomy, chemistry, physics, statistics, as well as to other areas of mathematics. Richards primary expertise in Modern Analysis is in the study of new classes of hypergeometric functions which generalize the classical theory developed by Euler, Gauss, Bessel, Ramanujan and many other famous scientists. Second, the principal investigator is interested in these new types of hypergeometric functions because of their fundamental importance in multivariate statistics. The research program will study these new hypergeometric functions and their properties with the aim of finding solutions to unsolved statistical problems which are of importance to applied researchers in medical and environmental fields.

摘要 理查兹 理查兹将继续他的计划研究超几何函数定义的矩阵空间和对称锥。 特别注意对称锥上的算子值超几何函数理论。 在该项目的第二部分，主要研究人员将继续他的研究应用这些特殊的功能，一般技术在调和分析和表示理论，多变量统计，总的积极性，概率不等式，以及相关的组合问题。 理查兹感兴趣的研究问题现代分析， 数学的一个分支，有两个原因。第一，现代分析 是数学的一个重要分支， 天文学，化学，物理学，统计学，以及其他 数学领域。 理查兹的主要专长是现代分析 是在研究新的超几何函数类，推广了经典理论的欧拉，高斯，贝塞尔， 拉马努金和许多其他著名科学家。二、校长 研究人员对这些新型超几何 函数，因为它们在多元 统计 该研究计划将研究这些新的超几何 函数及其性质，目的是找到解决方案 对应用具有重要意义的未解决的统计问题 医学和环境领域的研究人员。