Wandering subspaces and fusion frame generators for unitary systems

Abstract

This work is inspired by the study of wandering vectors and frame vectors for unitary systems. We investigate the structure and properties of complete wandering subspaces for unitary systems, and, in particular, we consider the unitary systems with a structure similar to wavelet systems. Given a unitary system with a complete wandering subspace, a necessary and sufficient condition for a closed subspace to be a Parseval fusion frame generator is obtained. Moreover, we study the dilation property for Parseval fusion frame generators for unitary groups.