论文标题
关于与Harish-Chandra的基本融合定理有关的问题
On a question related to a basic convergence theorem of Harish-Chandra
论文作者
论文摘要
Harish-Chandra在1958年关于区域球形功能的第一篇论文中证明了一种非常微妙的融合定理，这是他随后对他的Schwartz空间的定义和尖峰理论的定义。本文给出了基本证据，即对真正等级的一组，几组实际等级2（包括$ SO（n，2），sp_4（r）$和$ sp_4（c）$），$ gl（n，r）$和$ gl（n，c）$的相关积分收敛。实际上，在<cite> raphael </cite>中已证明了更强的结果。还研究了问题的应用。
In his first 1958 paper on zonal spherical functions Harish-Chandra proved an extremely delicate convergence theorem which was basic to his subsequent definition of his Schwartz space and his theory of cusp forms. This paper gives elementary proofs that a related integral converges for for groups of real rank one, several groups of real rank 2 (including $SO(n,2), Sp_4(R)$ and $Sp_4(C)$), $GL(n,R)$ and $GL(n,C)$. In fact, a stronger result has been proved in <cite>raphael</cite>. Applications of the question are also studied.
