Harmonic Analysis on Semisimple Lie Groups With Applications to Automorphic Forms

[摘要]kroetzthe PI打算继续他对李群表示的全纯方面的研究。重点将放在自同构形式和谐波分析的应用上。特别地，一个目标是获得自同构形式的傅里叶系数的估计。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群的表示理论对数学本身产生了深远的影响，特别是在分析和数论方面，以及理论物理，特别是量子力学和基本粒子物理方面。

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.