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On nodal sets and nodal domains on S^2 and R^2

Alexandre Eremenko·Dmitry Jakobson·Nikolai Nadirashvili
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Abstract

We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S^2. We also construct a solution of the equation Delta u=u in R^2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

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Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili. 2006-12-14. On nodal sets and nodal domains on S^2 and R^2. https://arxiv.org/abs/math/0611627

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