A Poisson formula for the Schrodinger operator

Rémi Carles (1) , Tohru Ozawa (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Department of Mathematics, Hokkaido University

We prove a nonlinear Poisson type formula for the Schrodinger group. Such a formula had been derived in a previous paper by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, energy-critical nonlinearities are allowed.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Rémi Carles, Tohru Ozawa. A Poisson formula for the Schrodinger operator. Journal of Fourier Analysis and Applications, 2008, 14 (3), pp.475-483. ⟨10.1007/s00041-008-9014-4⟩. ⟨hal-00170775⟩