Brown, Brian Malcolm and Evans, William Desmond and Wood, Ian (2013) Some spectral properties of Rooms and Passages domains and their skeletons. In: Holden, Helge and Simon, Barry and Teschl, Gerald, eds. Spectral analysis, differential equations and mathematical physics: a festschrift in honor of Fritz Gesztesy's 60th birthday. Proceedings of Symposia in Pure Mathematics, 87 . AMS, Providence, RI, USA, pp. 69-85. ISBN 978-0-8218-7574-2. (doi:10.1090/pspum/087/01438) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:44242)
| The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |
| Official URL: http://www.ams.org.chain.kent.ac.uk/books/pspum/08... |
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Abstract
In this paper we investigate spectral properties of Laplacians on Rooms and Passages domains. In the first part, we use Dirichlet-Neumann bracketing techniques to show that for the Neumann Laplacian in certain Rooms and Passages domains the second term of the asymptotic expansion of the counting function is of order $\sqrt{\lambda}$. For the Dirichlet Laplacian our methods only give an upper estimate of the form $\sqrt{\lambda}$. In the second part of the paper, we consider the relationship between Neumann Laplacians on Rooms and Passages domains and Sturm-Liouville operators on the skeleton.
| Item Type: | Book section |
|---|---|
| DOI/Identification number: | 10.1090/pspum/087/01438 |
| Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |
| Institutional Unit: | Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences |
| Former Institutional Unit: |
Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
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| Depositing User: | Ian Wood |
| Date Deposited: | 10 Nov 2014 17:53 UTC |
| Last Modified: | 20 May 2025 11:36 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/44242 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Wood, Ian.
| Creator's ORCID: |
 https://orcid.org/0000-0001-7181-7075
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