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

  • Rupert L. Frank

    Royal Institute of Technology St. Petersburg State University Department of Mathematics Department of Physics Lindstedtsvägen 25 Ul'yanovskaya 1, Petrodvorets, 10044 Stockholm, Sweden 198504 St. Petersburg, Russia
  • Roman G. Shterenberg

    Royal Institute of Technology St. Petersburg State University Department of Mathematics Department of Physics Lindstedtsvägen 25 Ul'yanovskaya 1, Petrodvorets, 10044 Stockholm, Sweden 198504 St. Petersburg, Russia
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering 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 . For non-negative we prove that is unitarily equivalent to the Neumann Laplacian . In general, there appear additional channels of scattering which are analyzed in detail.

Cite this article

Rupert L. Frank, Roman G. Shterenberg, On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Doc. Math. 9 (2004), pp. 57–77

DOI 10.4171/DM/157