Complex integral geometry

复杂积分几何

• 批准号: 0070816
• 负责人: Simon Gindikin
• 金额: $ 9.6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070816&HistoricalAwards=false
• 关键词: Complex; integral; geometry

AbstractGindikinThe focus of the proposal is the development of a method of complexhorospheras for real affine symmetric spaces, including real semisimpleLie groups. We anticipate to apply this method to the construction of themodels of series of representations and to the decomposition of the regularrepresentations on series on the language of Hardy spaces ofcohomology. As one of application we hope to give an integral geometrical proof of the product-formula for c-function of Harishi-Chandra. Another direction of my research is the investigation of geometrical and analytic properties ofthe crowns of Riemann symmetric spaces - their canonical Steinneighborhoods. Integral geometry is a branch of geometrical analysis whichinvestigates integral transforms associated with different geometricalstructures. The principal challenge is to find a geometrical setting, moregeneral than the group one, where it is possible to develop a non-abelianharmonic analysis. Another direction considers complex constructionsresponsible for the geometry of real affine symmetric spaces. Suchphenomena have roots in classical geometry of Poncelet and Pluecker.

AbstractGindikinThe建议的重点是发展的方法复horospheras的真实的仿射对称空间，包括真实的semisimpleLie群。我们期望将这种方法应用于表示级数的模型的构造和上同调哈代空间语言上级数的正则表示的分解。作为应用之一，我们希望给出Harishi-Chandra的c-函数乘积公式的一个积分几何证明。我的另一个研究方向是研究黎曼对称空间的冠的几何和分析性质--它们的典型Stein邻域。积分几何是几何分析的一个分支，它研究与不同几何结构相关的积分变换。主要的挑战是找到一个几何设置，更一般的比组一，在那里有可能开发一个非abelianharmonic分析。另一个方向考虑负责真实的仿射对称空间几何的复杂构造。这种现象的根源在经典几何的庞斯莱和Pluecker。