We study two-dimensional Hamiltonian systems of the form (•) y'(x) = zJH(x)y(x); x ∈ [s-; s+), where the Hamiltonian H is locally integrable on [s-; s+) and nonnegative, and J := (0 -1 | 1 0). The spectral theory of the equation changes depending on the growth of H towards the endpoint s+; the classical...
In many examples of de Branges spaces symmetry appears naturally. Pres-
ence of symmetry gives rise to a decomposition of the space into two
parts, the ‘even’ and the ‘odd’ part, which themselves can be regarded as
de Branges spaces. The converse question is to decide whether a given
space is the...
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...