Multipoint formulas for phase recovering from phaseless scattering data

Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We give formulas for phase recovering from appropriate monochromatic phaseless scattering data at 2n points in dimension d = 3 and in dimension d = 2. These formulas are recurrent and explicit and their precision is proportional to n. By this result we continue studies of [Novikov, Bull.Sci.Math. 139, 923-936, 2015], where formulas of such a type were given for n = 1, d ≥ 2.

Mots clés: Schrödinger equation; Helmholtz equation; Monochromatic scattering data; Phase recovering; Phaseless inverse scattering

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Roman Novikov. Multipoint formulas for phase recovering from phaseless scattering data. Journal of Geometric Analysis, 2021, 31 (2), pp.1965-1991. ⟨10.1007/s12220-019-00329-6⟩. ⟨hal-02119523⟩