Riemann xi function and modified Bessel functions

In a recent work of the author, a canonical system of differential equations with a diagonal Hamiltonian was constructed in connection with the Riemann zeta function. With this system an integral representation is associated in terms of modified Bessel functions for elements of the de Branges space corresponding to the canonical system. Such an integral representation is constructed for an element of the Hilbert space of the canonical system related to the Riemann zeta function modified in an appropriate way.