5 citations · 35 across the 32 of their papers we have counts for
4 papers · 1 filter
Courant-sharp Robin eigenvalues for the square and other planar domains
Katie Gittins, Bernard Helffer
This paper is devoted to the determination of the cases where there is equality in Courant's nodal domain theorem in the case of a Robin boundary condition. For the square, we part…
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…
Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is…
The spectrum of a Schrödinger operator in a wire-like domain with a purely imaginary degenerate potential in the semiclassical limit
Yaniv Almog, Bernard Helffer
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let denote an electric potential driven by a voltage drop between the conducting…