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On perturbations of the isometric semigroup of shifts on the semiaxis
We study perturbations of the semigroup of shifts
on with the property that belongs to a certain Schatten-von Neumann class \gS_p with .
We show that, for the unitary component in the Wold-Kolmogorov decomposition of
the cogenerator of the semigroup , {\it any singular}
spectral type may be achieved by \gS_1 perturbations. We provide an explicit
construction for a perturbation with a given spectral type based on the theory
of model spaces of the Hardy space . Also we show that we may obtain {\it
any} prescribed spectral type for the unitary component of the perturbed
semigroup by a perturbation from the class \gS_p with
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