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The phase retrieval problem for solutions of the Helmholtz equation

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierInstituto de Matematicas, Unidad Cuernavaca [UNAM-CUERNAVACA]
dc.contributor.authorPÉREZ-ESTEVA, Salvador
dc.date.accessioned2024-04-04T03:10:45Z
dc.date.available2024-04-04T03:10:45Z
dc.date.issued2017
dc.identifier.issn0266-5611
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193711
dc.description.abstractEnIn 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.
dc.description.sponsorshipAnalyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
dc.description.sponsorshipInitiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
dc.language.isoen
dc.publisherIOP Publishing
dc.subject.enphase retrieval
dc.subject.enHelmholtz equation
dc.title.enThe phase retrieval problem for solutions of the Helmholtz equation
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.identifier.arxiv1703.03742
bordeaux.journalInverse Problems
bordeaux.pageArticle 105007
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01486689
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01486689v1
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