Multi-orbital frames through model spaces

We characterize the normal operators $A$ on ${\mathrm{\ell }}^2$ and the elements $a^i \in \ell^2$,with$1\le i\le m$,suchthatthesequence$${ A^n a^1 , \ldots , A^n a^m }_{n\ge 0}$$ 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.