A duality between Schrödinger operators on graphs and certain Jacobi matrices
A formal series solution of the one-dimensional Schrödinger equation
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
A KAM-theorem for some nonlinear partial differential equations
A new approach to inverse spectral theory. I: Fundamental formalism.
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure.
A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.
A theory on perturbations of the Dirac operator.
About poles of the resolvent, in a model for a harmonic oscillator coupled with massless scalar bosons
Absolute Continuity of Hamiltonians with von Neumann Wigner Potentials II.
Accurate WKB Approximation for a 1D Problem with Low Regularity
2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings...
Adiabatic theory : stability of systems with increasing gaps
Adjoint and self-adjoint differential operators on graphs.
An Lp Estimate for the Difference of Derivatives of Spectral Expansions Arising by One-dimensional Schroedinger Operators
Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
Analyse semi-classique pour l'équation de Harper. II: Comportement semi-classique près d'un rationnel
Asymmetric bound states of differential equations in nonlinear optics
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Asymptotic normality of eigenvalues of random ordinary differential operators
Boundary value problems for ordinary differential equations with random coefficients are dealt with. The coefficients are assumed to be Gaussian vectorial stationary processes multiplied by intensity functions and converging to the white noise process. A theorem on the limit distribution of the random eigenvalues is presented together with applications in mechanics and dynamics.