NORM RETRIEVAL FROM SPATIOTEMPORAL SAMPLES

Abstract

The goal of this dissertation is to investigate norm retrievable frames having dynamical sampling structure, particularly those that fail the phase retrieval con- dition. We give several classifications to show how to construct norm retrievable frames dynamically, depending on the properties of the time-evolution operator. We show that norm retrievable frames generated by a single vector from a self- adjoint operator are most of the time phase retrievable frames. However, when we allow more generating vectors, there exist norm retrieval frames that do not do phase retrieval. We used two different subspace approaches to obtain these structures in real Hilbert spaces.