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

Abstract

In this paper, we revisit the analyses of Antonie Stern (1925) and Hans Lewy (1977) devoted to the construction of spherical harmonics with two or three nodal domains. Our method yields sharp quantitative results and a better understanding of the occurrence of bifurcations in the families of nodal sets.This paper is a natural continuation of our critical reading of A. Stern's results for Dirichlet eigenfunctions in the square, see arXiv:14026054.

Accepted for publication in "Monatshefte f{ü}r Mathematik"

References in corpus (1)

• Pleijel's nodal domain theorem for free membranes

Cited by in corpus (5)

• Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses
• Nodal domains in the square---the Neumann case
• On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern --
• Courant-sharp eigenvalues of a two-dimensional torus
• Some nodal properties of the quantum harmonic oscillator and other Schr{ö}dinger operators in ${\mathbb{R}}^2$