18 citations · 33 across the 5 of their papers we have counts for
5 papers
Upper bounds on eigenvalue multiplicities for spheres and plane domains revisited
Pierre Bérard, Bernard Helffer
We revisit two papers which appeared in 1999: M.~Hoffmann-Ostenhof, T.~Hoffmann-Ostenhof, and N.~Nadirashvili [Ann. Global Anal. Geom. 17 (1999) 43--48] and T.~Hoff\-mann-Ostenhof,…
On Courant's nodal domain property for linear combinations of eigenfunctions, Part I
Pierre Bérard, Bernard Helffer
According to Courant's theorem, an eigenfunction as\-sociated with the -th eigenvalue has at most nodal domains. A footnote in the book of Courant and Hilbert, states…
A. Stern's analysis of the nodal sets of some families of spherical harmonics revisited
Pierre Bérard, Bernard Helffer
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 y…
Remarks on J. Espinar's "Finite index operators on surfaces"
Pierre Bérard, Philippe Castillon
In this paper, we make some remarks on José Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].
Remarks on the boundary set of spectral equipartitions
Pierre Bérard, Bernard Helffer
Given a bounded open set in (or a compact Riemannian manifold with boundary), and a partition of by open sets , we consider the quantity $\max_j λ(ω…