Mathematical Sciences: Function Theory on Symmetric Spaces

数学科学：对称空间函数论

• 批准号: 9500794
• 负责人: Adam Koranyi
• 金额: $ 13.18万
• 依托单位: Research Foundation Of The City University Of New York (Lehman)
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500794&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Function; Theory; Symmetric

DMS-9500794 PI: Koranyi Koranyi will continue his investigation of quasiconformal maps in the context of Cauchy-Riemann manifolds. Part of the project is the study of Poisson transforms on vector bundles and their interaction with homogeneous differential operators. A second direction will be the study of boundary behavior for harmonic functions. A third direction will be the use of the harmonic analysis of the symmetric space of positive definite matrices to obtain methods of best estimation of a Gaussain distribution in the presence of some prior information. The analysis involved in this research rests on 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-9500794 PI：Koranyi Koranyi将继续他的调查拟共形映射的背景下柯西黎曼流形。 该项目的一部分是研究向量丛上的泊松变换及其与齐次微分算子的相互作用。 第二个方向将是调和函数的边界行为的研究。 第三个方向将是使用正定矩阵的对称空间的调和分析，以获得在存在一些先验信息的情况下高斯分布的最佳估计的方法。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，李群一直是世纪数学的主要主题之一。 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。