A gap in the continuous spectrum of a cylindrical waveguide with a periodic perturbation of the surface

Details A gap in the continuous spectrum of a cylindrical waveguide with a periodic perturbation of the surface A gap in the continuous spectrum of a cylindrical waveguide with a periodic perturbation of the surface

2009-10-29

arxiv.org/abs/0910.5679v1

Mathematische Nachrichten, vol. 283 (2010), p. 1222-1244

Mathematics

Spectral Theory

24 pages, 9 figures

Scientific paper

10.1002/mana.200910025

It is proved that small periodic singular perturbation of a cylindrical
waveguide surface may open a gap in the continuous spectrum of the Dirichlet
problem for the Laplace operator. If the perturbation period is long and the
caverns in the cylinder are small, the gap certainly opens.

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