4 citations · 8 across the 19 of their papers we have counts for
20 papers
Spectral Asymptotics of a Singular Harmonic Oscillator with Aharonov--Bohm Flux
Bernard Helffer, Ayman Kachmar, François Nicoleau
Motivated by a recent article of R. Vanlaere (2026), we investigate the spectral asymptotics of a singular harmonic oscillator arising from the radial reduction of the magnetic Sch…
Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows
Yaniv Almog, Bernard Helffer
We consider the spectrum of the Orr-Sommerfeld operator, which is obtained from the linearized Navier-Stokes (LNS) operator near a laminar flow in an infinite two-dimensional chann…
A Local-to-Global Propagation Principle for Dirichlet-to-Neumann Maps
Thierry Daudé, Alberto Enciso, Bernard Helffer +2
We establish four local-to-global propagation results for Dirichlet--to--Neumann maps. Our first two results are proved in the general setting of smooth compact Riemannian manifold…
Pleijel's theorem for a class of degenerate elliptic operators
Rupert L. Frank, Bernard Helffer
We prove an asymptotic upper bound on the number of nodal domains of eigenfunctions of a class of degenerate elliptic operators. Our proof yields the same constant as in Pleijel's…
A Sharp Regularity Threshold for Uniqueness in Riemannian Calderón-type Problems
Thierry Daudé, Alberto Enciso, Bernard Helffer +2
We prove a sharp regularity threshold for uniqueness in two anisotropic Calderón-type inverse problems in dimension . The main setting is the Riemannian Schrödinger problem…
A fresh look at the Peierls-Onsager substitution
Horia D. Cornean, Bernard Helffer, Radu Purice
We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-fram…
The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators
Horia D. Cornean, Bernard Helffer, Radu Purice
We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for…
On uniqueness of radial potentials for given Dirichlet spectra with distinct angular momenta
Damien Gobin, Benoît Grébert, Bernard Helffer +1
We consider an inverse spectral problem for radial Schrödinger operators with singular potentials. First, we show that the knowledge of the Dirichlet spectra for infinitely many an…
Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
Bernard Helffer, Ayman Kachmar, François Nicoleau
We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field li…
On the magnetic Dirichlet to Neumann operator on the exterior of the disk -- diamagnetism, weak-magnetic field limit and flux effects
Helffer Bernard, Nicoleau Francois
In this paper, we analyze the magnetic Dirichlet-to-Neumann operator (D-to-N map) on the exterior of the disk with respect to a magnetic potential $A_{b, ν}=A^b + A…
Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
Bernard Helffer, Ayman Kachmar, Francois Nicoleau
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…
Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Rupert L. Frank, Bernard Helffer, Ari Laptev
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results i…
On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--
Helffer Bernard, Nicoleau François
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…
A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider periodic (pseudo)differential {elliptic operators of Schrödinger type} perturbed by weak magnetic fields not vanishing at infinity, and extend our previous analysis in…
Eigenvalues of the Neumann magnetic Laplacian in the unit disk
Bernard Helffer, Corentin Léna
In this paper, we study the first eigenvalue of the magnetic Laplacian with Neumann boundary conditions in the unit disk in . There is a rather complete as…
The index of sub-laplacians: beyond contact manifolds
Magnus Goffeng, Bernard Helffer
In this paper we study the following question: do sub-Laplacian type operators have non-trivial index theory on Carnot manifolds in higher degree of nilpotency? The problem relates…
Global counterexamples to uniqueness for a Calderón problem with conductivities
Thierry Daudé, Bernard Helffer, Niky Kamran +1
Let , , be a fixed smooth bounded domain, and let be a smooth conductivity in . Consider a non-zero frequency which does not belong to…
Trace formulas for the magnetic Laplacian and Dirichlet to Neumann operator -- Explicit expansions --
Bernard Helffer, François Nicoleau
Inspired by a recent paper of G. Liu and X. Tan (2023), we would like to measure how the magnetic effect appears in the heat trace formula associated with the magnetic Laplacian an…
On Courant and Pleijel theorems for sub-Riemannian Laplacians
Rupert L. Frank, Bernard Helffer
We are interested in the number of nodal domains of eigenfunctions of sub-Laplacians on sub-Riemannian manifolds. Specifically, we investigate the validity of Pleijel's theorem, wh…
Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
Horia D. Cornean, Bernard Helffer, Radu Purice
In this paper we use some ideas from \cite{FG-97, G-06} and consider the description of Hörmander type pseudo-differential operators on (), including the cas…