Displaying similar documents to “Recovering Asymptotics at Infinity of Perturbations of Stratified Media”

On the real analyticity of the scattering operator for the Hartree equation

Changxing Miao, Haigen Wu, Junyong Zhang (2009)

Annales Polonici Mathematici

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We study the real analyticity of the scattering operator for the Hartree equation i ∂ t u = - Δ u + u ( V * | u | ² ) . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the...

Propagation of singularities in many-body scattering in the presence of bound states

András Vasy (1999)

Journées équations aux dérivées partielles

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In these lecture notes we describe the propagation of singularities of tempered distributional solutions u ∈ 𝒮 ' of ( H - λ ) u = 0 , where H is a many-body hamiltonian H = Δ + V , Δ ≥ 0 , V = ∑ a V a , and λ is not a threshold of H , under the assumption that the inter-particle (e.g. two-body) interactions V a are real-valued polyhomogeneous symbols of order - 1 (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is...