A Hamiltonian is a 2-by-2 positive semidefinite real symmetric matrix-valued function defined on an interval whose components are locally integrable. A canonical system is a first-order system of linear differential equations parametrized by complex numbers associated with a given Hamiltonian. This solution of a canonical system gives an entire function of the Hermite-Biehler class.

In this talk, we solve the inverse problem which recovers a Hamiltonian from a given function E in the Hermite-Biehler class under some special assumptions on E.

The method of the solution is similar to the solution of the inverse problem for strings given by M. G. Krein but is different. We will also explain the difference.