论文标题
Schrödinger方程在球体上的尖锐估计
Sharp Strichartz estimates for the Schrödinger equation on the sphere
论文作者
论文摘要
在这项贡献中，我们研究了与球体上与laplacian相关的Schrördinger方程，以尖锐的strichartz估计的形式。我们将使用纯粹使用[8]中证明的光谱投影（与球形谐波相关）的操作员规范的$ l^2 \ rightarrow l^p $频谱估算为我们的主要定理提供了简单的证明。在任意维度$ d \ geq 2 $的领域中，为初始数据建立了尖锐的规律性索引。
In this contribution we investigate the Schrördinger equation associated to the Laplacian on the sphere in the form of sharp Strichartz estimates. We will provided simple proofs for our main theorems using purely the $L^2\rightarrow L^p$ spectral estimates for the operator norm of the spectral projections (associated to the spherical harmonics) proved in [8]. A sharp index of regularity is established for the initial data in spheres of arbitrary dimension $d\geq 2$.
