Contributions to Books:
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,
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
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.