The Plancherel decomposition for a reductive symmetric space. I. Spherical functions
The Plancherel decomposition for a reductive symmetric space. I. Spherical functions
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还原对称空间的 Plancherel 分解。
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
H. Schlichtkrull
中科院分区：
文献类型：
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作者：
E. P. Ban;H. Schlichtkrull
证明了约化对称空间上球Schwartz函数的Plancherel公式。我们的出发点是球面光滑紧支撑函数的反演公式。后者的公式是较早获得的最连续的一部分Plancherel公式的手段剩余演算。在本文的过程中，我们还获得了新的证明的一致回火估计的归一化Eisenstein积分和的Maass-Selberg关系所满足的相关的C-函数。
We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized Eisenstein integrals and of the Maass–Selberg relations satisfied by the associated C-functions.