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.
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| Additional Information: | © 1992 Birkhäuser Verlag. Submitted: March 1991. The second author's research is partially funded under NSF grand number DMS-8801918. | |||||||||
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| 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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