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Sharp dispersive estimates for wave equation on lattice graphs with high dimension
Abstract
Schultz [Comm.~Pure~Appl.~Math., 1998] first established dispersive estimates for the fundamental solution of the discrete wave equation on lattice graphs Zd 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≥ 5. Moreover, the proof remains valid for the upper bound of the case for d=4.
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BibTeX
@misc{you2026sharp,
title = {{Sharp dispersive estimates for wave equation on lattice graphs with high dimension}},
author = {Zhe You and Xiongfeng Zhan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05930},
eprint = {2609.05930},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05930},
}
RIS
TY - UNPB
TI - Sharp dispersive estimates for wave equation on lattice graphs with high dimension
AU - Zhe You
AU - Xiongfeng Zhan
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05930
UR - https://arxiv.org/abs/2609.05930
AB - 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≥ 5. Moreover, the proof remains valid for the upper bound of the case for d=4.
ER -