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Published in:
2007 | OriginalPaper | Chapter
Canonical Differential Equations of Hilbert-Schmidt Type
Authors : Michael Kaltenbäck, Harald Woracek
Published in: Operator Theory in Inner Product Spaces
Publisher: Birkhäuser Basel
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A canonical system of differential equations, or Hamiltonian system, is a system of order two of the form
Jy′
(
x
) =
−zH
(
x
)
y
(
x
),
x
∈ ℝ
+
. We characterize the property that the selfadjoint operators associated to a canonical system have resolvents of Hilbert-Schmidt type in terms of the Hamiltonian
H
as well as in terms of the associated Titchmarsh-Weyl coefficient.