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Sharp Decay estimates for the discrete Fourth-Order Schrödinger Equation
Abstract
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.
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BibTeX
@misc{cheng2026sharp,
title = {{Sharp Decay estimates for the discrete Fourth-Order Schrödinger Equation}},
author = {Jiawei Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37300},
eprint = {2609.37300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37300},
}
RIS
TY - UNPB
TI - Sharp Decay estimates for the discrete Fourth-Order Schrödinger Equation
AU - Jiawei Cheng
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37300
UR - https://arxiv.org/abs/2609.37300
AB - 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.
ER -