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

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.

5 pages

References in corpus (1)

• Resolving isospectral "drums" by counting nodal domains

Cited by in corpus (10)

• Hearing shapes of drums - mathematical and physical aspects of isospectrality
• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
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• Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count
• Isospectral graphs with identical nodal counts
• Nodal domains of a non-separable problem - the right angled isosceles triangle
• Counting nodal domains on surfaces of revolution
• Inverse Nodal Problems
• On the Nodal Count Statistics for Separable Systems in any Dimension