The phase retrieval problem for solutions of the Helmholtz equation. (20th September 2017)

• Record Type: Journal Article
• Authors: Jaming, Philippe; Pérez-Esteva, Salvador
• Is Part Of: Inverse problems. Volume 33:Number 10(2017:Oct.)
• Publication Date: 2017-09-20
• Subjects: phase retrieval -- Helmholtz equation -- entire functions; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa8640
• Languages: English
• ISSNs: 0266-5611

Abstract

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.