On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators

  • Rupert L. Frank

    Mathematisches Institut LMU München Theresienstraße 39 80333 München, Germany
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators cover
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Abstract

We study spectral and scattering properties of the Laplacian in corresponding to the boundary condition for a wide class of periodic functions . The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators exist.

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Rupert L. Frank, On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Doc. Math. 8 (2003), pp. 547–565

DOI 10.4171/DM/150