实群和p-adic群的Howe-Moore性质
The Howe-Moore property for real and p-adic groups
摘要：
本文考虑了关于酉表示的系数在无穷远处为零的Howe-Moore性质的一个相对版本。我们刻画这个属性的遍历测度保持行动。对于线性李群或p-adic李群，我们还刻画了关于闭正规子群具有相对Howe-Moore性质的对偶。这涉及到，在一个方向上，结构的结果，局部紧群的所有适当的封闭特征子群是紧凑的，并在另一个方向上，一些结果消失在无穷大的振荡积分。
英文摘要：
We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear Lie groups or p-adic Lie groups, the pairs with the relative Howe-Moore Property with respect to a closed, normal subgroup. This involves, in one direction, structural results on locally compact groups all of whose proper closed characteristic subgroups are compact, and, in the other direction, some results about the vanishing at infinity of oscillatory integrals.
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