On nodal sets and nodal domains on S2 and R2

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Abstract

We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S2. We also construct a solution of the equation δu = u in ℝ2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

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Eremenko, A., Jakobson, D., & Nadirashvili, N. (2007). On nodal sets and nodal domains on S2 and R2. Annales de l’Institut Fourier, 57(7), 2345–2360. https://doi.org/10.5802/aif.2335

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