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math.AP2018
Sturm's theorem on the zeros of sums of eigenfunctions: Gelfand's strategy implemented
Pierre Bérard, Bernard Helffer
In the second section "Courant-Gelfand theorem" of his last published paper (Topological properties of eigenoscillations in mathematical physics, Proc. Steklov Institute Math. 273…
math.SP2018★ 2 cited
Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains. Application to the Extended Courant Property
Pierre Bérard, Bernard Helffer
In this paper, we prove that the Extended Courant Property fails to be true for certain smooth, strictly convex domains with Neumann boundary condition: there exists a linear combi…
math.SP2018★ 6 cited
On Courant's nodal domain property for linear combinations of eigenfunctions, Part II
Pierre Bérard, Bernard Helffer
Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first eigenfunctions has at most nodal domain…