离散四阶薛定谔方程的尖锐衰减估计
Sharp Decay estimates for the discrete Fourth-Order Schrödinger Equation
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中文总结 AI 辅助
本文在任意维数格点上建立离散四阶薛定谔方程的尖锐时间衰减估计，通过标量傅里叶分解与牛顿多面体方法，得到双调和传播子的衰减率$|t|^{-d/4}$。
中文摘要 AI 辅助
我们在任意维数格点上建立了离散四阶薛定谔方程的尖锐时间衰减估计，扩展了作者先前的工作\cite{C24}。在高维情形中，标量傅里叶分解将分析简化为一维振荡积分的乘积估计。由于该方法在低维情形下无法得到尖锐的衰减指数，我们还使用牛顿多面体来获得所需的均匀估计。特别地，双调和薛定谔传播子的尖锐衰减率为$|t|^{-d/4}$。
英文摘要
We establish sharp time-decay estimates for the discrete fourth-order Schrödinger equation on lattices of arbitrary dimension, extending the author's previous work \cite{C24}. In higher dimensions, scalar Fourier factorization reduces the analysis to product estimates for one-dimensional oscillatory integrals. Since this method does not yield the sharp decay exponents in low dimensions, we also use Newton polyhedra to obtain the required uniform estimates. In particular, the sharp decay rate for the biharmonic Schrödinger propagator is $|t|^{-d/4}$.
发表机构
- Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
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