一般线性群GL（n，R）上的抽象调和分析
Abstract Harmonic Analysis on the General Linear Group GL(n,R)
摘要：
考虑一般线性群，它不是连通的，而是有两个连通的分支，正行列式矩阵和负行列式矩阵。考虑其特殊线性群的Iwasawa分解。本文采用文[12]的技巧，推广了傅里叶变换的定义，得到了特殊线性群的Plancherel定理。此外，为了得到一般线性群的Plancherel定理，我们还证明了负行列式分支具有群结构，它同构于正行列式分支的群
英文摘要：
Consider the general linear group, which is not connected but rather has two connected components, the matrices with positive determinant and the ones with negative determinant. Consider the Iwasawa decomposition of its special linear group. We adopt the technique of the paper [12] to generalize the definition of the Fourier transform and to obtain the Plancherel theorem for the special linear group. Besides we prove that the component with negative determinant has a structure of group, which is isomorphic onto the group of the component with positive determinant in order to obtain the Plancherel theorem the general linear group
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