  A classical result of Duffin and Schaeffer gives conditions under which a
discrete collection of characters on $\mathbb{R}$, restricted to $E = (-1/2,
1/2)$, forms a Hilbert-space frame for $L^2(E)$. For the case of characters
with period one, this is just the Poisson Summation Formula. Duffin and
Schaeffer show that perturbations preserve the frame condition in this case.
This paper gives analogous results for the real Heisenberg group $H_n$, where
frames are replaced by operator-valued frames. The Selberg Trace Formula is
used to show that perturbations of the orthogonal case continue to behave as
operator-valued frames. This technique enables the construction of
decompositions of elements of $L^2(E)$ for suitable subsets $E$ of $H_n$ in
terms of representations of $H_n$.
