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Abstract view

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

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.