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arXiv · 2406.12868

Triple Products of Eigenfunctions and Spectral Geometry

Joe Schaefer
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Abstract

Using elementary techniques from Geometric Analysis, Partial Differential Equations, and Abelian $C^*$ Algebras, we uncover a novel, yet familiar, global geometric discriminant -- namely the indexed set of integrals of triple products of eigenfunctions of the Laplace-Beltrami operator, to precisely characterize which isospectral closed Riemannian manifolds are isometric.

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Joe Schaefer. 2024-04-16. Triple Products of Eigenfunctions and Spectral Geometry. https://doi.org/10.2139/ssrn.4793533

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