Mathematical Sciences: Poisson Integrals and Cayley Transforms on Bounded Homogeneous Domains in Cn

数学科学：Cn 有界齐次域上的泊松积分和凯莱变换

• 批准号: 9306222
• 负责人: Richard Penney
• 金额: $ 6.04万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306222&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Poisson; Integrals; Cayley

Penney will continue his investigation to determine what aspects of the harmonic analysis of Hermitian symmetric spaces generalize to non-symmetric situations. Particular questions yet to be resolved are (a) how to characterize the Poisson integrals of hyperfunctions on the boundary and (b) how to treat unbounded domains. The first step will be to determine if there exist on a bounded homogeneous domain a system of differential operators which annihilates the Gindikin-Poisson kernel. The basic idea behind Penney's project can be seen already in the motion group of the line, which consists of translations and reflection about zero. The quotient of the motion group by the reflection subgroup is naturally isomorphic to the line. Similarly, more general geometric objects can be realized as the quotient of a transformation group by a certain subgroup. This introduces natural classes of group invariant operators on the geometric space, and analysis is developed using eigenfunctions of the group invariant operators.

彭尼将继续调查，以确定 埃尔米特对称空间的调和分析 推广到非对称情况。 有特殊问题吗 要解决的问题是（a）如何刻画Poisson积分 （B）如何处理无界的 域. 第一步将是确定是否存在 有界齐性区域微分算子系统 这会消除Gindikin-Poisson核。 Penney项目背后的基本思想已经可以看出 在由平移组成的直线运动组中， 反射率为零。 运动群的商， 反射子群自然同构于直线。 类似地，更一般的几何对象可以实现为 变换群与某个子群的商。 这 介绍了自然类的群不变算子上的 几何空间，并分析开发使用本征函数 群不变算子