3 documents found

Article / Chapter
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2013-11-22

A growth condition for Hamiltonian systems related with Krein strings

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...
Article / Chapter
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2013-04-11

Symmetry in de Branges almost Pontryagin spaces

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...
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2011-12-13

Reparametrizations of non trace-normed Hamiltonians

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...