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

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.

arXiv comment12 pages, 4 figures

Cited by in corpus (1)

• A. Stern's analysis of the nodal sets of some families of spherical harmonics revisited