Riemannian manifolds with maximal eigenfunction growth
Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.
Riemannsche Flächen mit Eigenwerten in (0, ...).
Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.
Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.
Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators
We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in norm, at Lebesgue points and almost everywhere. We also prove localization results.
Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture. II
Rotationally invariant periodic solutions of semilinear wave equations.
Scattering amplitude for the Schrödinger equation with strong magnetic field
In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
Scattering and resolvent on geometrically finite hyperbolic manifolds with rational cusps
These notes summarize the papers [8, 9] on the analysis of resolvent, Eisenstein series and scattering operator for geometrically finite hyperbolic quotients with rational non-maximal rank cusps. They complete somehow the talk given at the PDE seminar of Ecole Polytechnique in october 2005.
Scattering and spectral theory for Stark Hamiltonians in one dimension.
Scattering by two convex bodies
Scattering for 1D cubic NLS and singular vortex dynamics
We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions form a family of evolving regular curves in that develop a singularity in finite time, indexed by a parameter . We consider curves that are small regular perturbations of for a fixed time . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of local existence...
Scattering for a dispersive charge transfer model
Scattering frequencies and Gevrey 3 singularities.
Scattering matrix for asymptotically euclidean manifolds
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
Scattering phases and density of states for exterior domains
Scattering problem for nonlinear Schrödinger equations
Scattering problems in a domain with small holes.
In this paper, we consider a family of scattering problems in perforated unbounded domains Ωε. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.
Scattering properties for a pair of Schrödinger type operators on cylindrical domains
Strong asymptotic completeness is shown for a pair of Schrödinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre’s method within the context of pseudo-selfadjoint operators.