Phase Retrieval for Nilpotent Groups

Journal of Fourier Analysis and Applications, vol. 29

Abstract

Abstract We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected Lie groups, and for finite groups. We prove by induction that in the Lie group case, all irreducible representations do phase retrieval. For the finite group case, we mostly focus on p -groups. Here our main result states that every irreducible representation of an arbitrary p -group with exponent p and size $$\le p^{2+p/2}$$ ≤ p 2 + p / 2 does phase retrieval. Despite the fundamental differences between the two settings, our inductive proof methods are very similar.

Authors 2

1. Hartmut Führ corresponding Aachen Lehrstuhl für Geometrie und Analysis

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen University, 52056, Aachen, Germany

2. Vignon Oussa

   Bridgewater State University

   Affiliation as printed

   Department of Mathematics, Bridgewater State University, Bridgewater, MA, 02234, USA