Some problems in inverse scattering theory
Some remarks on eigenfunction expansions for Schrödinger operators with non-local potentials.
Some Remarks on Transmutation, Scattering Theory, and Special Functions.
Some solved and unsolved canonical problems of diffraction theory
Spectral Analysis of the Laplacian in Domains with Cylinders.
Spectral and scattering theory for symbolic potentials of order zero
Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials
Spectral and scattering theory in deformed optical wave guides.
Spectral asymptotics for manifolds with cylindrical ends
The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to , where is the dimension of the manifold.
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...
Spectral properties of vaguely elliptic pseudo differential operators with momentum dependent long range potentials using time dependent scattering theory - II.
Spectral theory of corrugated surfaces
We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.
Stabilisation pour l'équation des ondes dans un domaine extérieur.
On s'intéresse dans cet article, a la stabilisation de l'équation des ondes dans un domaine extérieur avec condition de Dirichlet...
Stability of the inverse problem in potential scattering at fixed energy
We prove an estimate of the kind , where , is the scattering amplitude related to the compactly supported potential at a fixed energy level const., , and is a suitably defined norm.
Stark hamiltonians with periodic potentials
Stationary Scattering Theory for Time-dependent Hamiltonians.
Strichartz inequality for orthonormal functions
We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
Structure of S-matrices for three body Schrödinger operators
Sul comportamento asintotico della soluzione di un problema di radiazione