We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy f ′ (0) = 0.Alternatively, these results can be interpreted as interpolation results for H ∞ (V ), where V is the intersection of the bidisk with an algebraic variety.We use an analysis of C*-envelopes to show that these same conditions do not suffice for matrix interpolation.
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Davidson et al. (2009) studied this question.