Remark on Essential Selfadjointness of Dirac Operators with Coulomb Potentials.
Remarks on an eigenvalue problem associated with the -Laplace operator.
Remarks on essential self-adjointness of Schrödinger operators with singular electrostatic potentials.
Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients
We consider Schrödinger operators on with variable coefficients. Let be the free Schrödinger operator and we suppose is a “short-range” perturbation of . Then, under the nontrapping condition, we show that the time evolution operator: can be written as a product of the free evolution operator and a Fourier integral operator which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...
Remarks on the non self-adjoint Schrödinger operator
Remarks on uniqueness results of the first eigenvalue of the p-Laplacian
Remarque sur la conjecture de Weyl.
Remarque sur un article de Marcel Berger : «Sur une inégalité pour la première valeur propre du laplacien»
Remarques sur la conjecture de Weyl
Representations of Compact Lie Groups and Elliptic Operators.
Resolvent and Scattering Matrix at the Maximum of the Potential
2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing...
Resolvent estimates for 2-dimensional perturbations of plane Couette flow.
Resonance expansions in wave propagation
Resonance functions of two-body Schrödinger operators
Resonance theory for periodic Schrödinger operators
Resonance theory of two-body Schrödinger operators
Resonance with respect to the Fučík spectrum.
Resonances and Spectral Shift Function near the Landau levels
We consider the 3D Schrödinger operator where , is a magnetic potential generating a constant magneticfield of strength , and is a short-range electric potential which decays superexponentially with respect to the variable along the magnetic field. We show that the resolvent of admits a meromorphic extension from the upper half plane to an appropriate Riemann surface , and define the resonances of as the poles of this meromorphic extension. We study their distribution near any fixed...
Résonances de Rayleigh en dimension 2
Nous étudions les résonances de Rayleigh créées par un obstacle strictement convexe à bord analytique en dimension 2. Nous montrons qu’il existe exactement deux suites de résonances et convergeant exponentiellement vite vers l’axe réel dans un voisinage polynomial de l’axe réel, et exponentiellement proches d’une suite de quasimodes réels. De plus, est un symbole analytique d’ordre 0 en la variable dont on donne le premier terme du développement. Nous construisons pour cela des quasimodes...
Résonances de Rayleigh en dimension deux