Schatten空间中规范规范正交系和振荡积分算子的谱簇界
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces
摘要：
本文将紧黎曼流形上Laplace-Beltrami算子的Sogge的$L^p$谱簇界推广到正交函数系.并讨论了这些新界的最优性。这些谱簇界遵循Schatten型界的振荡积分运营商。
英文摘要：
We generalize the $L^p$ spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.
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