Harmonic Analysis on Semisimple Lie Groups With Applications to Automorphic Forms

派建议继续他对李群表示的全纯方面的研究。重点介绍自同构形式和调和分析的应用。特别地，一个目标是获得关于自同构形式的傅立叶系数的估计。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

ABSTRACTKroetzThe PI proposes to continue his investigations on the holomorphic aspects of representationsof Lie groups. An emphasis will be taken towards applications to automorphic forms and harmonic analysis. In particular, one objective is to obtain estimates on the Fourier coefficients of automorphic forms. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had aprofound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.