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Spectral properties of Neumann Laplacian of horns

Davies, E. B. and Simon, B. (1992) Spectral properties of Neumann Laplacian of horns. Geometric and Functional Analysis, 2 (1). pp. 105-117. ISSN 1016-443X. doi:10.1007/BF01895707. https://resolver.caltech.edu/CaltechAUTHORS:20180314-071625612

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Abstract

We study the Neumann Laplacian of unbounded regions in ℝ^n with cusps at infinity so that the corresponding Dirichlet Laplacian has compact resolvent. Typical of our results is that of the region {(x, y)_∈ℝ^2 ∥xy|<1} the Neumann Laplacian has absolutely continuous spectrum [0, ∞) of uniform multiplicity four and an infinity of eigenvalues E_0 < E_ 1 ≤... → ∞ and that for the region {(x, y)_∈ℝ^2∥y|≤ e^-^(∣x∣)}, it has absolutely continuous spectrum [1/4, ∞) of uniform multiplicity 2 and an infinity of eigenvalues E_0 = 0 < E_1 ≤... → ∞. We use the Enss theory with a suitable asymptotic dynamics.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF01895707DOIArticle
https://link.springer.com/article/10.1007/BF01895707PublisherArticle
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
Additional Information:© 1992 Birkhäuser Verlag. Submitted: March 1991. The second author's research is partially funded under NSF grand number DMS-8801918.
Funders:
Funding AgencyGrant Number
NSFDMS-8801918
Subject Keywords:Spectral Property; Continuous Spectrum; Compact Resolvent; Asymptotic Dynamic; Unbounded Region
Issue or Number:1
DOI:10.1007/BF01895707
Record Number:CaltechAUTHORS:20180314-071625612
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180314-071625612
Official Citation:Davies, E.B. & Simon, B. Geometric and Functional Analysis (1992) 2: 105. https://doi.org/10.1007/BF01895707
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85297
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Mar 2018 16:11
Last Modified:15 Nov 2021 20:27

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