Multi-orbital Frames Through Model Spaces

Abstract

We characterize the normal operators A on \(\ell ^2\) and the elements \(a^i \in \ell ^2\), with \(1\le i\le m\), such that the sequence $$\begin{aligned} \{ A^n a^1, \ldots , A^n a^m \}_{n\ge 0} \end{aligned}$$is a frame. The characterization makes strong use of the pseudo-hyperbolic metric of \( {{\mathbb {D}}} \) and is given in terms of the backward shift invariant subspaces of \(H^2( {{\mathbb {D}}} )\) associated to finite products of interpolating Blaschke products.