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 $$\{A^n{a}^1,\dots ,A^n{a}^m{\}}_{n\ge 0}$$ 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.