On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering

Academic Article

Abstract

  • We study spectral and scattering properties of the Laplacian H (σ) = -Δ in L2(ℝ+2) corresponding to the boundary condition ∂u/∂ν + σu = 0 for a wide class of periodic functions σ. For non-negative σ we prove that H(σ) is unitarily equivalent to the Neumann Laplacian H(0). In general, there appear additional channels of scattering which are analyzed in detail.
  • Published In

    Author List

  • Frank RL; Shterenberg RG
  • Start Page

  • 57
  • End Page

  • 77
  • Volume

  • 9
  • Issue

  • 1