Reparametrizations of non trace-normed Hamiltonians

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, i.e. satis_es 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 of reparametrization in detail.


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