Isospectrality and Heat Content

Authors

Emily Dryden, Bucknell UniversityFollow
Michiel van den Berg, University of BristolFollow
Thomas Kappeler, Universitat ZurichFollow

Publication Date

2014

Description

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 Schrodinger operators acting in L²[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Journal

Bulletin of the London Mathematical Society

First Page

793

Last Page

808

Department

Mathematics

DOI

10.1112/blms/bdu035

Recommended Citation

Dryden, Emily; van den Berg, Michiel; and Kappeler, Thomas. "Isospectrality and Heat Content." Bulletin of the London Mathematical Society (2014) : 793-808.