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 $\pi$. 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.

Cited by in corpus (2)

• Injectivity of Gabor phase retrieval from lattice measurements
• Arithmetic progressions and holomorphic phase retrieval