Remarks on "Resolving isospectral `drums' by counting nodal domains"
Spectral Theory
2010-07-21 v1 Mathematical Physics
math.MP
Abstract
In [3] the authors studied the 4-parameter family of isospectral flat 4-tori T^\pm(a,b,c,d) discovered by Conway and Sloane. With a particular method of counting nodal domains they were able to distinguish these tori (numerically) by computing the corresponding nodal sequences relative to a few explicit tuples (a,b,c,d). In this note we confirm the expectation expressed in [3] by proving analytically that their nodal count distinguishes any 4-tuple of distinct positive real numbers.
Cite
@article{arxiv.0709.3745,
title = {Remarks on "Resolving isospectral `drums' by counting nodal domains"},
author = {Jochen Bruening and David Klawonn and Christof Puhle},
journal= {arXiv preprint arXiv:0709.3745},
year = {2010}
}
Comments
5 pages