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 Kwon and Lee (RIMS Kokyuroku Bessatsu 70:33–58, 2018). A sharp index of regularity is established for the initial data in spheres of arbitrary dimension \(d\ge 2\).

中文翻译：

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Sharp Strichartz对球体上Schrödinger方程的估计

在这一贡献中，我们以锐利的Strichartz估计形式研究了与球上的拉普拉斯算子相关的Schrördinger方程。我们将仅使用权重为Kwon和Lee（RIMS Kokyuroku Bessatsu）的光谱投影（与球谐函数相关）的算术范数的\（L ^ 2 \ rightarrow L ^ p \）光谱估计，为主要定理提供简单的证明。70：33–58，2018）。在任意维度\（d \ ge 2 \）的球体内为初始数据建立了鲜明的正则性索引。