A Constrained Nevanlinna-Pick Interpolation Problem

By K. Davidson, Vern I. Paulsen, M. Raghupathi, Dinesh Singh. 2007

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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 $H^{\infty}(V),$ 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.

Subfields: Applied Mathematics, Mathematical Physics

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