COMPLEX FOURIER ANALYSIS ON A NILPOTENT LIE GROUP
COMPLEX FOURIER ANALYSIS ON A NILPOTENT LIE GROUP
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幂零李群的复傅立叶分析
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Lie Group
中科院分区：
文献类型：
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作者：
Lie Group
。设 G 为单连通幂零李群，具有复化 Gc。 G 上的函数是 G 在 L2(G) 上的左正则表示的解析向量，在本文中通过其解析延拓到 Gc 的双重表征以及其 L2 傅立叶变换的性质来确定。这些函数的解析延拓由傅里叶反演公式给出。为左正则表示的整个向量的密集空间给出了显式构造。在 G = R 的情况下，这为 Paley 和 Wiener 关于带中全纯函数的结果提供了群论设置。
. Let G be a simply-connected nilpotent Lie group, with complexification Gc. The functions on G which are analytic vectors for the left regular representation of G on L2(G) are determined in this paper, via a dual characterization in terms of their analytic continuation to Gc, and by properties of their L2 Fourier transforms. The analytic continuation of these functions is shown to be given by the Fourier inversion formula. An explicit construction is given for a dense space of entire vectors for the left regular representation. In the case G = R this furnishes a group-theoretic setting for results of Paley and Wiener concerning functions holomorphic in a strip.