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# Spectral theory for the Neumann Laplacian on planar domains with horn-like ends

Published:1997-04-01
Printed: Apr 1997
• Julian Edward
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## Abstract

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.
 MSC Classifications: 35P25 - Scattering theory [See also 47A40] 58G25 - unknown classification 58G25