The phase retrieval problem for solutions of the Helmholtz equation
Résumé
In this paper we consider the phase retrieval problem for Herglotz functions, that is, solutions of the Helmholtz equation ∆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 = cv 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 non vanishing mean.
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