论文标题
关于紧凑型谎言组的傅里叶限制类型问题
On Fourier restriction type problems on compact Lie groups
论文作者
论文摘要
在本文中，我们获得了紧凑型谎言组的傅立叶限制类型问题的新结果。我们首先就其Laplace-Beltrami特征值提供了$ l^p $估计不可约字符的估计值，因此，为连接不变的差异操作员提供了一些尖锐的$ l^p $估计值。然后，我们改进了Schrödinger方程量表不变的Strichartz估算的先前指数范围，并根据其特征值类似于Tori上已知的界限，提供了Laplace-Beltrami本征的新的$ l^p $边界。我们证明这些结果的一个关键成分是对最大圆环中Weyl Alcove的Barycentric-Speciallasical细分。在此细分的每个组成部分上，我们对字符和指数总和进行分析，以及Hardy-Littlewood和Kloosterman的圆方法。
In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a consequence provide some sharp $L^p$ estimates of joint eigenfunctions for the ring of conjugate-invariant differential operators. Then we improve upon the previous range of exponent for scale-invariant Strichartz estimates for the Schrödinger equation, and provide new $L^p$ bounds of Laplace-Beltrami eigenfunctions in terms of their eigenvalue similar to known bounds on tori. A key ingredient in our proof of these results is a barycentric-semiclassical subdivision of the Weyl alcove in a maximal torus. On each component of this subdivision we carry out the analysis of characters and exponential sums, and the circle method of Hardy--Littlewood and Kloosterman.
