Mathematical Sciences: First-Order Elliptic Systems in Harmonic Analysis

数学科学：调和分析中的一阶椭圆系统

• 批准号: 8812414
• 负责人: John Gilbert
• 金额: $ 5.52万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-02-15 至 1991-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8812414&HistoricalAwards=false
• 关键词: Mathematical; Sciences; First; Order; Elliptic

This project provides support for continuing work on boundary problems associated with families of first-order systems of overdetermined, elliptic differential equations. The corresponding differential operators originate in the generalized potential theory in harmonic analysis on both Euclidean and Riemannian symmetric spaces. Applications to Euclidean Hardy-space theory and to explicit realization of unitarizable exceptional representations of semi-simple Lie groups will be made. Because of emphasis on group invariances, polynomial invariant theory will play an increasingly important role in these investigations. Further work on the group-theoretic connections will also be carried out. The ellipticity of the systems ensures the completeness of the normed spaces in which the solutions can be found while the over-determinedness allows one to study just the harmonic real parts of the (complex) functions under consideration.

该项目为继续研究与超定椭圆微分方程一阶系统族相关的边界问题提供支持。相应的微分算子起源于欧几里得对称空间和黎曼对称空间的调和分析中的广义势论。将应用到欧几里德哈代空间理论以及半单李群的可统一化例外表示的显式实现。 由于强调群不变性，多项式不变理论将在这些研究中发挥越来越重要的作用。 关于群论联系的进一步工作也将进行。系统的椭圆性确保了可以在其中找到解决方案的规范空间的完整性，而超定性允许人们仅研究所考虑的（复）函数的调和实部。