Jakšić, V. and Molčanov, S. and Simon, B. (1992) Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps. Journal of Functional Analysis, 106 (1). pp. 59-79. ISSN 0022-1236. doi:10.1016/0022-1236(92)90063-O. https://resolver.caltech.edu/CaltechAUTHORS:20170809-113325669
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Abstract
We study the eigenvalue asymptotics of a Neumann Laplacian −Δ_N^Ω in unbounded regions Ω of R^2 with cusps at infinity (a typical example is Ω = {(x, y) ϵR^2: x > 1, ¦y¦< e^(−x)^2}) and prove that N_E(−Δ_N^Ω) ~ N_E(H_v) +E2Vol(Ω), where H_v is the canonical one-dimensional Schrödinger operator associated to the problem. We establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a Dirichlet Laplacian −Δ_D^Ω for a class of cusp-type regions of infinite volume.
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| Additional Information: | © 1992 Elsevier Inc. Received 17 June 1991. Communicated by L. Gross. We are greateful to E. B. Davies for useful discussions and to L. Romans for comments on the manuscript. S. Moleanov thanks B. Simon and D. Wales for their hospitality at Caltech, where this work was done. | |||||||||
| Issue or Number: | 1 | |||||||||
| DOI: | 10.1016/0022-1236(92)90063-O | |||||||||
| Record Number: | CaltechAUTHORS:20170809-113325669 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170809-113325669 | |||||||||
| Official Citation: | V Jakšić, S Molčanov, B Simon, Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps, Journal of Functional Analysis, Volume 106, Issue 1, 15 May 1992, Pages 59-79, ISSN 0022-1236, https://doi.org/10.1016/0022-1236(92)90063-O. (http://www.sciencedirect.com/science/article/pii/002212369290063O) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 80019 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 09 Aug 2017 20:48 | |||||||||
| Last Modified: | 15 Nov 2021 17:52 |
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