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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

R2 v1 2026-06-21T09:21:01.451Z