论文标题
关于爱因斯坦 - 克莱因 - 戈登系统的傅立叶分析：傅立叶常数的生长和衰变
On the Fourier analysis of the Einstein-Klein-Gordon system: Growth and Decay of the Fourier constants
论文作者
论文摘要
我们考虑$（1 + 3）$ - 尺寸的爱因斯坦方程，其负宇宙恒定与球形对称，无质量标量场耦合，并在抗DE安静的空间周围进行研究扰动。我们得出共鸣系统，挑选消失的世俗术语，并讨论与小除数有关的问题。最重要的是，我们严格地为所有相互作用系数建立了渐近行为（在大多数情况下）。后者基于与线性化操作员以及某些振荡积分相关的征函数的均匀估计。
We consider the $(1 + 3)$-dimensional Einstein equations with negative cosmological constant coupled to a spherically-symmetric, massless scalar field and study perturbations around the Anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic behaviour for all the interaction coefficients. The latter is based on uniform estimates for the eigenfunctions associated to the linearized operator as well as on some oscillatory integrals.
