Five Hilbert space models related to the Riemann zeta function

In a recent work of the author, a de Branges space was constructed, as well as an operator on it with spectrum, which coincides with the set of non-trivial zeros of the Riemann zeta function after a rotation of the complex plane. Also the canonical system corresponding to the de Branges space was constructed. In this paper we construct a natural factorization of the unitary operator that realizes the unitary correspondence between the Hilbert space of the canonical system and the de Branges space, as the superposition of four unitary operators.