# Some spectral properties of Rooms and Passages domains and their skeletons

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. (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)

 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. (Contact us about this Publication) Official URLhttp://www.ams.org.chain.kent.ac.uk/books/pspum/08...

## 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 Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Ian Wood 10 Nov 2014 17:53 UTC 10 Nov 2014 17:53 UTC https://kar.kent.ac.uk/id/eprint/44242 (The current URI for this page, for reference purposes)