Spectral theory for the Neumann Laplacian on planar domains with horn-like ends
Printed: Apr 1997
The spectral theory for the Neumann Laplacian on planar domains with
symmetric, horn-like ends is studied. For a large class of such domains,
it is proven that the Neumann Laplacian has no singular continuous
spectrum, and that the pure point spectrum consists of eigenvalues
of finite multiplicity which can accumulate only at $0$ or $\infty$.
The proof uses Mourre theory.
35P25 - Scattering theory [See also 47A40]
58G25 - unknown classification 58G25