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The three-point Pick-Nevanlinna interpolation problem on the polydisc (1505.03763v4)
Published 14 May 2015 in math.CV
Abstract: We give a characterization for the existence of a holomorphic interpolant on the unit polydisc $\mathbb{D}n,$ $n\geq 2,$ for prescribed three-point Pick--Nevanlinna data. One of the key steps is a characterization for the existence of an interpolant that is a rational inner function on $\mathbb{D}n.$ The latter reduces the search for a three-point interpolant to finding a single rational inner function that satisfies a type of positivity condition and arises from a polynomial of a very special form. This in turn relies on a pair of results, which are of independent interest, on the factorization of rational inner functions.