Harmonic Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One
Harmonic Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One
复制标题
实一阶半单李群调和分布的调和分析
DOI：
10.1090/surv/031/02
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发表时间：
1970
影响因子：
1.3
通讯作者：
J. Arthur
中科院分区：
文献类型：
--
作者：
J. Arthur
总结。设G是实半单李群。Harish-Chandra定义了G上的Schwartz空间V[G]。G上的回火分布是RG上的连续线性泛函)。如果G的实数阶等于1，Harish-Chandra已经发表了I^(G)[3(K)，5241]的Plcherel公式的一个版本。我们将傅里叶变换映射限制到%(G)，并计算V(G)空间的像[定理31。这使得我们可以发展关于G上回火分布的调和分析理论[定理51。摘要
SUMMARY. Let G be a real semisimple Lie group. Harish-Chandra has defined the Schwartz space, V[G), on G. A tempered distribution on G is a continuous linear functional on RG). If the real rank of G equals one, Harish-Chandra has published a version of the Plancherel formula for I^(G) [3(k), 5241. We restrict the Fourier transform map to %(G), and we compute the image of the space V(G) [Theorem 31. This permits us to develop the theory of harmonic analysis for tempered distributions on G [Theorem 51. Summary