On nodal sets and nodal domains on S 2 and 2
Annales de l'Institut Fourier, Volume 57 (2007) no. 7, p. 2345-2360
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 Δu=u in 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.
On étudie les configurations topologiques possibles d’ensembles nodaux, en particulier, le nombre de leurs composantes, pour les harmoniques sphériques sur S 2 . Nous construisons aussi une solution de l’équation Δu=u dans  2 qui possède seulement deux domaines nodaux. Cette équation est considérée dans l’étude des fonctions propres à haute énergie.
DOI : https://doi.org/10.5802/aif.2335
Classification:  58J50,  11J70,  35P20,  81Q50
Keywords: Laplacian, nodal sets, nodal domains, spherical harmonic, topological configuration
@article{AIF_2007__57_7_2345_0,
     author = {Eremenko, Alexandre and Jakobson, Dmitry and Nadirashvili, Nikolai},
     title = {On nodal sets and nodal domains on $\mathbf{S^2}$ and ${\mathbb{R}}^{\mathbf{2}}$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {7},
     year = {2007},
     pages = {2345-2360},
     doi = {10.5802/aif.2335},
     zbl = {pre05249488},
     mrnumber = {2394544},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_7_2345_0}
}
Eremenko, Alexandre; Jakobson, Dmitry; Nadirashvili, Nikolai. On nodal sets and nodal domains on $\mathbf{S^2}$ and ${\mathbb{R}}^{\mathbf{2}}$. Annales de l'Institut Fourier, Volume 57 (2007) no. 7, pp. 2345-2360. doi : 10.5802/aif.2335. https://aif.centre-mersenne.org/item/AIF_2007__57_7_2345_0/

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