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arXiv · 0709.3745

Remarks on "Resolving isospectral `drums' by counting nodal domains"

Jochen Bruening·David Klawonn·Christof Puhle
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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.

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Jochen Bruening, David Klawonn, Christof Puhle. 2007-09-24. Remarks on "Resolving isospectral `drums' by counting nodal domains". https://doi.org/10.1088/1751-8113/40/50/n01

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