A Note on the Phase Retrieval of Holomorphic Functions
Classical Analysis and ODEs
2023-06-22 v2 Complex Variables
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 . 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.
Keywords
Cite
@article{arxiv.2009.02061,
title = {A Note on the Phase Retrieval of Holomorphic Functions},
author = {Rolando Perez},
journal= {arXiv preprint arXiv:2009.02061},
year = {2023}
}