M. Langer, H. Woracek:

"Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints";

in: "ASC Report 18/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 85.

Part I of this paper deals with two-dimensional canonical systems

y′(x) = yJH(x)y(x), x ∈ (a, b), whose Hamiltonian H is non-negative and locally integrable, and where Weyl´s limit point case takes place at both endpoints a and b.

We investigate a class of such systems defined by growth restrictions on H towards a.

canonical system, Sturm-Liouville equation, singular potential, direct and inverse spectral theorems, Pontryagin space, de Branges space

http://www.asc.tuwien.ac.at/preprint/2015/asc18x2015.pdf

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