复约化群上的全纯调和分析
Holomorphic harmonic analysis on complex reductive groups
摘要：
定义了复约化群上全纯函数的全纯傅里叶变换，证明了类似于傅里叶反演公式的一些性质，并给出了一些应用。全纯傅里叶变换的定义利用了$K$ -容许测度的概念。证明了$K$ -容许测度是丰富的，全纯傅里叶变换的定义与$K$ -容许测度的选择无关.
英文摘要：
We define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties like the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of $K$-admissible measures. We prove that $K$-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of $K$-admissible measures.
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