On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
نویسندگان
چکیده
We study spectral and scattering properties of the Laplacian H = −∆ in L2(R+) corresponding to the boundary condition ∂u ∂ν + σu = 0 for a wide class of periodic functions σ. The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators W±(H ,H) exist. 2000 Mathematics Subject Classification: Primary 35J10; Secondary 35J25, 35P05, 35P25.
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