Scattering by periodic surfaces

  title={Scattering by periodic surfaces},
  author={Albert William S{\'a}enz},
If Ω⊆ Rν (ν?2) is an exterior domain containing a half‐space and contained in a half space, we prove that the wave operators W± = s‐limt→±∞ exp(itH) Jexp(−itH0) are partial isometries and that the invariance principle W±(φ) = W± holds for suitable real functions φ on R (’’admissible’’ functions). Here H0 is the negative (distributional) Laplacian in L2(Rν) (ν?2); H is HD or HN , the negative Dirichlet or Neumann Laplacians in H = L2(Ω), respectively; J is an appropriate identification operator… CONTINUE READING