The phase retrieval problem for solutions of the Helmholtz equation. (20th September 2017) - Jaming, Philippe; Pérez-Esteva, Salvador
Abstract: In this paper we consider the phase retrieval problem for solutions of the Helmholtz equation Δ u + λ 2 u = 0 on domains Ω ⊂ R d, d ⩾ 2 . In dimension d = 2, if u, v are two such solutions then | u | = | v | implies that either u = c v or u = c v ̄ for some c ∈ C with | c | = 1 . In dimension d ⩾ 3, the same conclusion holds under some restriction on u and v : either they are real valued or zonal functions or have a non vanishing mean.