On the spectrum of the Neumann Laplacian of long-range horns: a note on the Davies-Simon theorem
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- by V. Jakšić PDF
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Abstract:
For a class of regions with cusps (e.g., $\Omega = \{ (x,y):x > 1,|y| < \exp ( - {x^\alpha })\} ,\;0 < \alpha < 1)$) 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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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