发表机构
School of Mathematics, East China University of Science and Technology; School of Mathematics and Statistics, Beijing Jiaotong University（华东理工大学数学学院; 北京交通大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对高维格图上离散波动方程，完整解决了所有剩余维度的色散估计，并证明对每个 $d\geq 5$ 估计是尖锐的，且证明对 $d=4$ 的上界也有效。
AI 中文摘要
Schultz [Comm.~Pure~Appl.~Math., 1998] 首次建立了格图 $\Z^d$ 上离散波动方程基本解在 $d=2,3$ 时的色散估计，这可视为欧几里得波动方程经典色散估计的离散类比。他的结果被 Bi、Cheng 和 Hua 推广至 $d=4$ 和 $5$。本文对所有剩余维度（包括 $d=5$）给出了完整解答。我们的估计对每个 $d\geq 5$ 都是尖锐的。此外，该证明对 $d=4$ 情形的上界依然有效。
英文摘要
Schultz [Comm.~Pure~Appl.~Math., 1998] first established dispersive estimates for the fundamental solution of the discrete wave equation on lattice graphs $\Z^d$ for $d=2,3$, which can be seen as a discrete analogue of the classical dispersive estimate for the Euclidean wave equation. His result was extended by Bi, Cheng and Hua to $d=4$ and $5$. In this paper, we give complete answers to all the remaining dimensions, including $d=5$. Our estimate is sharp for every $d\geq 5$. Moreover, the proof remains valid for the upper bound of the case for $d=4$.
