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Isospectrality and heat content


Van Den Berg, Michiel; Dryden, Emily; Kappeler, Thomas (2014). Isospectrality and heat content. Bulletin of the London Mathematical Society, 46(4):793-808.

Abstract

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrödinger operators acting in L2[0, 1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Abstract

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrödinger operators acting in L2[0, 1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:07 Oct 2014 08:51
Last Modified:05 Apr 2016 18:24
Publisher:Oxford University Press
ISSN:0024-6093
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1112/blms/bdu035

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