Arithmetic progressions and holomorphic phase retrieval

Author:

Liehr Lukas1

Affiliation:

1. Faculty of Mathematics University of Vienna Vienna Austria

Abstract

AbstractWe study the determination of a holomorphic function from its absolute value. Given a parameter , we derive the following characterization of uniqueness in terms of rigidity of a set : if is a vector space of entire functions containing all exponentials , then every is uniquely determined up to a unimodular phase factor by if and only if is not contained in an arithmetic progression . Leveraging this insight, we establish a series of consequences for Gabor phase retrieval and Pauli‐type uniqueness problems. For instance, is a uniqueness set for the Gabor phase retrieval problem in , provided that is a suitable perturbation of the integers.

Publisher

Wiley

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