论文标题
真实球形空间的Plancherel分解的最连续部分
The most continuous part of the Plancherel decomposition for a real spherical space
论文作者
论文摘要
在本文中，我们对$ l^{2}（z）$的最连续部分的Plancherel分解进行了精确描述。我们的出发点是Delorme，Knop，Krötz和Schlichtkrull最近建造的Bernstein Morphisms。最连续的部分分解为统一主序列表示的直接组成部分。我们在这些主要系列中对$ h $ invariant功能进行了明确的结构。我们表明，对于通用感应数据，多样性空间等于$ h $ invariant函数的完整空间。最后，我们通过完善Maass-Selberg关系来确定多样性空间上的内部产品。
In this article we give a precise description of the Plancherel decomposition of the most continuous part of $L^{2}(Z)$ for a real spherical homogeneous space $Z$. Our starting point is the recent construction of Bernstein morphisms by Delorme, Knop, Krötz and Schlichtkrull. The most continuous part decomposes into a direct integral of unitary principal series representations. We give an explicit construction of the $H$-invariant functionals on these principal series. We show that for generic induction data the multiplicity space equals the full space of $H$-invariant functionals. Finally, we determine the inner products on the multiplicity spaces by refining the Maass-Selberg relations.
