Harmonic Analysis on Semisimple Lie Groups With Applications to Automorphic Forms

半单李群的调和分析及其在自守形式中的应用

• 批准号: 0097314
• 负责人: Bernhard Kroetz
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0097314&HistoricalAwards=false
• 关键词: Harmonic; Analysis; Semisimple; Lie; Groups

ABSTRACTKroetzThe PI proposes to continue his investigations on the holomorphic aspects of representationsof Lie groups. An emphasis will be taken towards applications to automorphic forms and harmonic analysis. In particular, one objective is to obtain estimates on the Fourier coefficients of automorphic forms. 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 aprofound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

摘要Kroetz的PI建议继续他的调查全纯方面的表示李群。重点将采取对应用程序的自守形式和谐波分析。特别是，一个目标是获得自守形式的傅立叶系数的估计。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。作为利用系统中固有的对称性的数学工具，李群的表示论对数学本身，特别是在分析和数论方面，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。