(untitled) (Journal of Mathematical Study, 2025)
In this paper, we establish a decay estimate for the discrete four-order Schrödinger equation on the hexagonal triangulation with γ=0. The proof is based on the uniform estimates of oscillatory integrals, as developed by Karpushkin, along with a key result by Varchenko. Our result is to show the l^1→l^∞ dispersive decay rate is ⟨t⟩^−σ for any 0<σ<12. Additionally, we provide estimates for the inhomogeneous discrete fourth-order Schrödinger equation with γ=0.