Remling's Theorem on canonical systems

Density of Schrödinger Weyl–Titchmarsh m functions on Herglotz functions

“…The reason to have projection matrices P ϕ is the asymptotic behavior of solutions to (2). Indeed, de Branges, Krein and Langer [7,19] showed that solutions to (10)…”

“…It is well known that Weyl theory can be applied to a canonical system in a similar way to that for Schrödinger operators (see e.g. [2]). More precisely, it is possible to choose f n = (f n,1 , f n,2 ) t which are H n -integrable solutions to (10)…”

“…To be self-contained we are going to prove Proposition 5.1 by following the argument in [2]. The extension of his argument from H to H, however, is necessary, especially to deal with ∞.…”

“…The extension of his argument from H to H, however, is necessary, especially to deal with ∞. As a cost of this extension, the proof becomes much longer than that in [2].…”