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

Pierre Bérard (1) , Bernard Helffer (2, 3)

1 IF - Institut Fourier
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 LMJL - Laboratoire de Mathématiques Jean Leray

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. This is a natural continuation of our critical reading of A. Stern's results for Dirichlet eigenfunctions in the square \cite{BeHe}

Mots clés: Nodal lines; Nodal domains; Courant theorem.

Mots clés: Courant theorem

Domaines: Géométrie différentielle [math.DG]; Théorie spectrale [math.SP]

Pierre Bérard, Bernard Helffer. A.~Stern's analysis of the nodal sets of some families of spherical harmonics revisited. 2014. ⟨hal-01026363v1⟩