德西特空间上的球面分布及其谱奇异性
Spherical Distributions on the De Sitter Space and their Spectral Singularities
AI总结：
本文综述德西特空间上球面分布作为半全纯核边界值的构造，并探讨其与反射正定性、洛伦兹群连通分支表示及波前集奇异性的联系。
摘要：
球面分布是德西特空间上具有某种不变性的拉普拉斯–贝尔特拉米算子的特征分布。设 G'=O(1,n;R) 为洛伦兹群，H'=O(1,n-1;R) 为其子群。作者 Olafsson 和 Sitiraju 构造了这些 H'-不变的球面分布，作为某些半全纯核的边界值。在这篇综述文章中，我们将探讨这些核与反射正定性以及群 G=SO(1,n;R)_e（洛伦兹群的连通分支）的表示之间的联系。我们还将从波前集的角度讨论球面分布的奇异性。
英文摘要：
A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju have constructed the spherical distributions, which are $H'$-invariant, as boundary values of some sesquiholomorphic kernels. In this survey article we will explore the connections of these kernels with reflection positivity and representations of the group G = SO(1,n;R)_e, which is the connected component of the Lorentz group. We will also discuss the singularities of spherical distributions in terms of their wavefront set.
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