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

作者：Berard P^*; Helffer B

来源：Monatshefte fur Mathematik, 2016, 180(3): 435-468.

DOI：10.1007/s00605-015-0788-6

• Nodal lines
• Nodal domains
• Courant theorem

In this paper, we revisit the analyses of Stern (Bemerkungen ber asymptotisches Verhalten von Eigenwerten und Eigenfunktionen, W. Fr. Kaestner, Gttingen, 1925) and Lewy (Commun Partial Differ Equ 2(12): 1233-1244, 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.

• 出版日期2016-7