Dispersion for the Schr{ö}dinger equation on the line with short-range array of delta potentials

We study dispersive properties of the one-dimensional Schr{ö}dinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator obtained by perturbing the free Laplacian on the line with a real-valued sequence of Dirac delta potentials and belonging to weighted $\mathrm{\ell }$^1(Z) spaces. Under suitable decay assumptions on the coupling constants and in the absence of a zero-energy resonance, we establish the L^1 ® $\to$ L^$\mathrm{\infty }$ ® dispersive estimate with decay rate |t|^{-1/2} for the associated Schr{ö}dinger group. The proof relies on a limiting absorption principle in weighted spaces, explicit representation of the resolvent kernel in terms of Jost solutions and Born series expansion of the Friedrichs extension of the perturbed operator.