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Abstract: Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary andsufficient conditions for the existence of a solution to the Nevanlinna-Pickinterpolation problem on the unit disk with the additional restriction that theinterpolant should have the value of its derivative at the origin equal tozero. This concrete mild generalization of the classical problem isprototypical of a number of other generalized Nevanlinna-Pick interpolationproblems which have appeared in the literature for example, on afinitely-connected planar domain or on the polydisk. We extend the results ofDavidson-Paulsen-Raghupathi-Singh to the setting where the interpolant isallowed to be matrix-valued and elaborate further on the analogy with thetheory of Nevanlinna-Pick interpolation on a finitely-connected planar domain.



Author: J.A. Ball, V. Bolotnikov, S. ter Horst

Source: https://arxiv.org/







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