We consider a Hamiltonian system of the form y (x)= jh (x) y (x), with a locally integrable and
nonnegative 2 x 2-matrix-valued Hamiltonian (H). I n the literature dealing with the operator
theory of such equations, it is often required in addition that the Hamiltonian H is trace-
normed, ie, satisfies tr (x)≡ 1. Ho wever, in many examples this property does not hold. The
general idea is that one can reduce to the trace-normed case by applying a suitable change
of scale (reparametrization). In this paper we justify this idea and work out the notion of …

We consider a Hamiltonian system of the form y0 (x)= JH (x) y (x), with a locally integrable
and nonnegative 2× 2-matrix valued Hamiltonian H (x). In the literature dealing with the
operator theory of such equations, it is often required in addition that the Hamiltonian H is
trace-normed, ie satisfies trH (x) 1. However, in many examples this property does not hold.
The general idea is that one can reduce to the trace-normed case by applying a suitable
change of scale (reparametrization). In this paper we justify this idea and work out the notion …