Parameterization of Intertwining Liftings and its Applications
In this chapter it is shown that the set of all intertwining liftings with tolerance γ in the commutant lifting theorem is parameterized by a natural set of contractive analytic operator-valued functions. A Redheffer scattering interpolation of this parameterization is given. In the final three sections, state space formulas are given for the Redheffer scattering matrix parameterizing the set of all solutions for the standard left Nevanlinna-Pick, Nehari and two-block interpolation problems.
KeywordsInterpolation Problem Open Unit Disc Unilateral Shift Pointwise Stable Mobius Transformation
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