A Note on the Phase Retrieval of Holomorphic Functions - Archive ouverte HAL
Journal Articles Canadian Mathematical Bulletin Year : 2020

A Note on the Phase Retrieval of Holomorphic Functions

Abstract

We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then f = g up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of π. We also prove that if f and g are functions in the Nevanlinna class, and if |f | = |g| on the unit circle and on a circle inside the unit disc, then f = g up to the multiplication of a unimodular constant.
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Dates and versions

hal-02929358 , version 1 (03-09-2020)
hal-02929358 , version 2 (03-10-2020)

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Public Domain

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Rolando Perez Iii. A Note on the Phase Retrieval of Holomorphic Functions. Canadian Mathematical Bulletin, 2020, ⟨10.4153/S000843952000082X⟩. ⟨hal-02929358v2⟩

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