By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass.
"On dispersion for Klein Gordon equation with periodic potential in 1D." Hokkaido Math. J. 37 (4) 627 - 645, November 2008. https://doi.org/10.14492/hokmj/1249046361