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.
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(KAR id:44242)

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Official URL http://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 |
---|---|

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 10 Nov 2014 17:53 UTC |

Last Modified: | 16 Feb 2021 12:57 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/44242 (The current URI for this page, for reference purposes) |

Wood, Ian: | https://orcid.org/0000-0001-7181-7075 |

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