5 citations · 5 across the 7 of their papers we have counts for
8 papers
Capacity estimates and improved lower bounds for the inner radius of nodal domains
Philippe Charron
We show that for every closed, smooth manifold of dimension , there exists such that any nodal domain of a Laplace eigenfunction with eigenvalue contain…
On the concentration of the Fourier coefficients for products of Laplace-Beltrami eigenfunctions on real-analytic manifolds
Philippe Charron, François Pagano
On a closed analytic manifold , let be the eigenfunctions of with eigenvalues and let be a finite product of Laplace-Beltrami eigenfun…
Sturm-Hurwitz Theorem for quantum graphs
Ram Band, Philippe Charron
We prove upper and lower bounds for the number of zeroes of linear combinations of Schrödinger eigenfunctions on metric (quantum) graphs. These bounds are distinct from both the in…
The inner radius of nodal domains in high dimensions
Philippe Charron, Dan Mangoubi
We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue on a -dimensional closed Riemannian manifold contains a ball of radius $cλ^{-1/2}(\logλ)^…
Pleijel's theorem for Schrödinger operators
Philippe Charron, Corentin Léna
We are concerned in this paper with the real eigenfunctions of Schrödinger operators. We prove an asymptotic upper bound for the number of their nodal domains, which implies in par…
Non-boundedness of the number of super level domains of eigenfunctions
Pierre Bérard, Philippe Charron, 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…
Pleijel's theorem for Schrödinger operators with radial potentials
Philippe Charron, Bernard Helffer, Thomas Hoffmann-Ostenhof
In 1956 . Pleijel gave his celebrated theorem showing that the inequality in Courant's theorem on the number of nodal domains is strict for large eigenvalues of the Laplacian. T…
A Pleijel-type theorem for the quantum harmonic oscillator
Philippe Charron
We prove a Pleijel-type theorem for the asymptotic behaviour of the number of nodal domains of eigenfunctions of the quantum harmonic oscillator in any dimension.