Collaborative Research: An Analysis of Characters and Matrix Coefficients for Representations of Real Classical Lie Groups

协作研究：实经典李群表示的特征和矩阵系数分析

• 批准号: 0200724
• 负责人: Tomasz Przebinda
• 金额: $ 9.6万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0200724&HistoricalAwards=false
• 关键词: Collaborative; Research; Analysis; Characters; Matrix

AbstractPrzebindaThe aim of this project is to study the characters and matrix coefficients of the representations of the classical groups from the view point of the theory of reductive dual pairs. In particular of interest are formulas for the characters in terms of the natural moment maps, and the wave front sets. Regarding the matrix coefficients, the central question is to decide which absolutely integrable positive definite matrix coefficients have positive integral, and corollaries regarding the preservation of unitarity under Howe's correspondence.We shall apply the ideas sketched above to signal processing. Specifically we are interested in the information compression and denoising of signals which are well balanced in the time-frequency domain.

该项目的AbstractPrzeBindathe目的是从还原双对理论的角度研究古典组表示的字符和基质系数。特别是感兴趣的是角色的公式，从自然力矩图和波浪前组来看。关于矩阵系数，中心问题是确定哪些绝对可集成的正定矩阵系数具有正等位置，并且有关在Howe的对应关系下保存单位性的推论。我们应将上述想法应用于信号处理。具体而言，我们对在时频域中保持平衡的信号的信息压缩和降解感兴趣。