Jean-Claude Guillot

Inverse spectral theory for a singular Sturm-Liouville operator on [0, 1]

This is a correction to our article in the Journal of Differential Equations, Volume 76(1988).

Quantum electrodynamics of relativistic bound states with cutoffs

We consider a Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.

Théorie spectrale de la propagation des ondes acoustiques dans un milieu stratifié perturbé

Abstract In this article the spectral analysis of the self adjoint operator governing the propagation acoustic waves in a perturbed stratified medium is given. Both a medium whose sound speed is a short range perturbation of that of a stratified medium and a stratified medium exterior to a compact set are considered. The basic tool is a division theorem for the self adjoint operator governing the propagation of acoustic waves in a pure stratified medium.

Gaps of One-Dimensional Periodic AKNS Systems

Consider the periodic AKNS operator (see [AKNS] and [Zak-Sha])

Inverse scattering at fixed energy for layered media

\left( {\begin{array}{*{20}{c}} 0 & { - 1} \\ 1 & 0 \\ \end{array} } \right)\frac{d}{{dx}} + \left( {\begin{array}{*{20}{c}} { - q\left( x \right)} & {p\left( x \right)} \\ {p\left( x \right)} & {q\left( x \right)} \\ \end{array} } \right), x \in \mathbb{R}

Steady-State Wave Propagation in Simple and Compound Acoustic Waveguides*

(1) where p(x) and q(x) are real valued potentials in H loc 1 (ℝ) or in H loc 2 (ℝ) such that

Spectral Theory for a Mathematical Model of the Weak Interaction: The Decay of the Intermediate Vector Bosons W±, II

\begin{array}{l}p\left( {x + 1} \right) = p\left( x \right)\\\begin{array}{*{20}{c}}{x \in R}\\{q\left( {x + 1} \right) = q\left( x \right)}\\{} \end{array} \end{array}