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Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends

Published online by Cambridge University Press:  20 November 2018

Julian Edward
Julian Edward*
Affiliation:
Department of Mathematics, Florida International University, Miami, Florida 33199, U.S.A. e-mail: edwardj@fiu.edu
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Abstract

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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 ∞. The proof uses Mourre theory.

Keywords

35P2558G25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 232 - 262
Copyright
Copyright © Canadian Mathematical Society 1997

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