Mathematical Sciences: Harmonic Analysis and Group Representation

数学科学：调和分析和群表示

• 批准号: 9500907
• 负责人: Hongming Ding
• 金额: $ 4.86万
• 依托单位: Saint Louis University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500907&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Analysis; Group

DMS-9500905 PI: Ding Ding will study analytic continuation of operator-valued Bessel functions on symmetric cones and symmetric Siegel domains; in particular, operator valued Bessel functions on boundary components of these domains. Using analytic continuation of Bessel functions, he will study the decomposition of the harmonic representation of automorphism groups of these domains. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

DMS-9500905 主要研究者：丁 丁将研究分析延续算子值贝塞尔函数的对称锥和对称西格尔域;特别是，算子值贝塞尔函数的边界组件这些域。 使用解析延续贝塞尔函数，他将研究分解的调和表示的自同构群的这些领域。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。