Function Theory on Symmetric Spaces

对称空间函数论

• 批准号: 9732599
• 负责人: Adam Koranyi
• 金额: $ 10.31万
• 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: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732599&HistoricalAwards=false
• 关键词: Function; Theory; Symmetric; Spaces

Abstract Koranyi Koranyi will continue his investigations of harmonic analysis on Riemannian symmetric spaces with an emphasis on harmonic functions and relations with complex analysis. Of particular interest will be solving the long-standing problem of a local Fatou theorem for harmonic functions on symmetric spaces. This will be approached through the theory of discrete buildings. A second direction of research will be the use of quasiconformal maps in several complex variables. A primary concern here is the extension of quasiconformal maps of the boundary of a strictly pseudoconvex domain to the interior as symplectic quasiconformal maps with respect to the Bergman metric. The analysis involved in this research rests on the theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, which has beenone 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.

摘要古兰经 Koranyi将继续他的调查调和分析黎曼对称空间的重点调和函数和关系与复杂的分析。 特别感兴趣的将是解决长期存在的问题的局部法图定理调和函数的对称空间。 这将通过离散建筑物的理论来处理。 第二个研究方向将是在多个复变量中使用拟共形映射。 这里的一个主要问题是扩展的拟共形映射的边界的严格pseudoconvular域的内部辛拟共形映射的Bergman度量。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，它是20世纪世纪数学的重要课题之一。 作为利用系统中固有对称性的数学工具，李群的表示论对数学本身产生了深远的影响，特别是在分析和数论方面，对理论物理特别是量子力学和基本粒子物理也产生了深远的影响。