Spectral and scattering properties at thresholds for the Laplacian in a   half-space with a periodic boundary condition
  For the scattering system given by the Laplacian in a half-space with a periodic boundary condition, we derive resolvent expansions at embedded thresholds, we prove the continuity of the scattering matrix, and we establish new formulas for the wave operators. 
S. Richard and R. Tiedra de Aldecoa
math-ph math.FA math.MP math.SP