Abstract
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, i.e., 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 reparametrization in detail.
Mathematics Subject Classification (2000). Primary 34B05; Secondary 34L40, 47E05.
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Winkler, H., Woracek, H. (2012). Reparametrizations of Non Trace-normed Hamiltonians. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_40
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DOI: https://doi.org/10.1007/978-3-0348-0297-0_40
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