On nodal sets and nodal domains on S^2 and R^2
Spectral Theory
2012-02-07 v2 Analysis of PDEs
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.
Cite
@article{arxiv.math/0611627,
title = {On nodal sets and nodal domains on S^2 and R^2},
author = {Alexandre Eremenko and Dmitry Jakobson and Nikolai Nadirashvili},
journal= {arXiv preprint arXiv:math/0611627},
year = {2012}
}
Comments
12 pages, 4 figures