Complex integral geometry

本文的重点是发展实仿射对称空间，包括实半单Lie群的复球方法。我们期望将这一方法应用于上同调的Hardy空间语言上的级数表示模型的构造和级数正则表示的分解。作为应用之一，我们希望给出Harishi-Chandra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Riemann对称空间的冠的几何和解析性质--它们的标准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比第一组更一般的几何环境，在那里可以进行非简谐分析。另一个方向认为复数结构负责实仿射对称空间的几何。这些现象起源于庞斯莱和普鲁克的经典几何学。

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.