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On the spectrum of the Neumann Laplacian of long-range horns: a note on the Davies-Simon theorem


Author: V. Jakšić
Journal: Proc. Amer. Math. Soc. 119 (1993), 663-669
MSC: Primary 35P05; Secondary 35P25, 47A10, 47F05
DOI: https://doi.org/10.1090/S0002-9939-1993-1155600-7
MathSciNet review: 1155600
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Abstract: For a class of regions with cusps (e.g., $ \Omega = \{ (x,y):x > 1,\vert y\vert < \exp ( - {x^\alpha })\} ,\;0 < \alpha < 1)$) we show that $ {\sigma _{\operatorname{ac} }}( - \Delta _N^\Omega ) = [0,\infty )$ of uniform multiplicity one, $ {\sigma _{\operatorname{sing} }}( - \Delta _N^\Omega ) = \emptyset $, and $ {\sigma _{\operatorname{pp} }}( - \Delta _N^\Omega )$ consists of a discrete set of embedded eigenvalues of finite multiplicity.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1155600-7
Article copyright: © Copyright 1993 American Mathematical Society

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