Cyclic frames in finite-dimensional Hilbert spaces

Abstract: Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi et al. in \cite{ACM} and subsequent papers; they are particularly interesting due to their attractive properties in the context of erasure problems. By applying an alternative approach, we are able to shed new light on general dynamical frames as well as cyclic frames. In particular, we provide a characterization of dynamical frames, which in turn leads to a characterization of cyclic frames.