  Let $\mu$ be a measure on the real line $\mathbb{R}$ such that
$\int_{\mathbb{R}}\frac{d\mu(t)}{1+t^2} < \infty$ and let $a>0$. Assume that
the norms $\|f\|_{L^2(\mathbb{R})}$ and $\|f\|_{L^2(\mu)}$ are comparable for
functions $f$ in the Paley-Wiener space $PW_{a}$ and that $PW_a$ is dense in
$L^2(\mu)$. We reconstruct the canonical Hamiltonian system $JX' = zHX$ such
that $\mu$ is the spectral measure for this system.
