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

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

2006-11-21

arxiv.org/abs/math/0611627v2

Ann. Inst. Fourier, 57 (2007) 2345-2360

Mathematics

Spectral Theory

12 pages, 4 figures

Scientific paper

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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