Mathematical Sciences: Function Theory on Symmetric Spaces.

数学科学：对称空间函数论。

• 批准号: 8701530
• 负责人: Adam Koranyi
• 金额: $ 7.31万
• 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: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701530&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Function; Theory; Symmetric

This project represents a continuation of work on the theory of quasiconformal mappings on the Heisenberg group. Problems of global distortion, extension theorems and relaxation of smoothness conditions present in existing results will be treated. The same problems will also be considered on general CR manifolds with positive Levi form with applications to complex variable theory. A second thrust will be made in the direction of harmonic analysis on symmetric cones. With the use of Jordan algebras a theory of special functions will be developed. In addition, boundary behavior of harmonic functions on symmetric spaces will be analyzed through the use of Tits buildings. In this context a generalized Luzin area function will be sought. Finally, the generalization of the geometric properties of the Heisenberg group to so-called H-type groups will be carried out. The work planned relates to several areas of mathematics, including classical function theory and quasiconformal mapping. Other applications to the gamma function, boundary behavior in potential theory and the Plancherel theorem can be made. New insights into the holomorphic equivalence problem are possible

本课题是Heisenberg群上拟共形映射理论研究的继续。将处理现有结果中存在的全局扭曲、延拓定理和光滑性条件的松弛问题。同样的问题也将被考虑在具有正Levi形式的一般CR流形上，并应用于复变量理论。第二个推力将朝向对称圆锥的调和分析方向进行。利用Jordan代数，将发展出一种特殊函数理论。此外，还将利用Tits建筑物来分析对称空间上调和函数的边界行为。在此背景下，将寻求广义Luzin面积函数。最后，将Heisenberg群的几何性质推广到所谓的H型群。计划的工作涉及几个数学领域，包括经典函数论和拟共形映射。对于伽马函数、位势理论中的边界行为和普朗彻尔定理，也可以有其他的应用。对全纯等价问题的新见解是可能的