Spectral functions of a canonical system of order $2n$

The author describes a set of pseudospectral functions of the canonical system of differential equations
$$ \frac{dW(x,\lambda)}{dx}=i\lambda JH(x)W(x,\lambda), \qquad W(0,\lambda)=E_{2n}, $$
where $0\leqslant x\leqslant l<\infty$, $H(x)=H^*(x)\geqslant 0$, $J=\begin{bmatrix}0&E_n\\E_n&0\end{bmatrix}$.
In terms of the Hamiltonians $H(x)$, conditions are given under which the pseudospectral functions are spectral functions.