On dispersion decay for discrete wave equations (Q2517051)

The paper is devoted to the one-dimensional discrete wave equation \[ \ddot u(t)=-H(u),\,\,\,t\in\mathbb{R},\leqno(1) \] where \(H:=-\Delta_L+q\), \(q\) is a real potential, and \(\Delta_L\) is the discrete Laplacian given by \((\Delta_L u)_n=u_{n+1}-2u_n+u_{n-1}\), \(n\in\mathbb{Z}\). Under some assumptions on the potential \(q\), the author obtains some dispersion estimates for the solutions of equation \((1)\) in the non-singular case.