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H. Winkler, H. Woracek:
"On semibounded canonical systems";
in: "ASC Report 27/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

We present two inverse spectral relations for canonical differential
equations Jy0(x) = −zH(x)y(x), x 2 [0,L): Denote by QH the Titchmarsh-
Weyl coefficient associated with this equation. We show: If the Hamiltonian
H is on some interval [0, ) of the form
H(x) =
"
v(x)2 v(x)
v(x) 1
«
,
with a nondecreasing function v, then limx&0 v(x) = limy!+1 QH(iy). If H is
of the above form on some interval [l,L), then limx%L v(x) = limz%0 QH(z).
In particular, these results are applicable to semibounded canonical systems,
or canonical systems with a finite number of negative eigenvalues, respectively.

canonical (Hamiltonian) system, Titchmarsh-Weyl coefficient, Inverse

http://www.asc.tuwien.ac.at/preprint/2007/asc27x2007.pdf