Sign retrieval in spaces of variable bandwidth

Abstract

The aim of this paper is to get a deeper understanding of the spaces of variable bandwidth introduced by Gr{ö}chenig and Klotz (What is variable bandwidth? Comm. Pure Appl. Math., 70 (2017), 2039-2083). In particular, we show that when the variation of the bandwidth is modeled by a step function with a finite number of jumps, then, the sign retrieval principle applies.