论文标题
在等级的一个对称空间的非竞争类型的频谱投影的不确定性原理
An uncertainty principle for spectral projections on rank one symmetric spaces of noncompact type
论文作者
论文摘要
让$ g $成为有限中心的非竞争半圣母谎言组。令$ x = g/k $为关联的里曼尼亚对称空间，并假设$ x $是等级的。与Laplace-Beltrami操作员相关的光谱投影由$p_λf= f \astφ_λ$给出，其中$φ_λ$是$ x $上的基本球形函数。在本文中，我们证明了$p_λf$的Ingham类型不确定性原理。此外，在与Dunkl Laplacian相关的光谱投影的情况下，获得了类似的结果。
Let $G $ be a noncompact semisimple Lie group with finite centre. Let $X=G/K$ be the associated Riemannian symmetric space and assume that $X$ is of rank one. The spectral projections associated to the Laplace-Beltrami operator are given by $P_λf =f\ast Φ_λ$, where $Φ_λ$ are the elementary spherical functions on $X$. In this paper, we prove an Ingham type uncertainty principle for $P_λf$. Moreover, similar results are obtained in the case of spectral projections associated to Dunkl Laplacian.
