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arXiv · 1503.03091

Three-point Nevanlinna Pick problem in the polydisc

Lukasz Kosinski
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Abstract

It is very elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are just left inverses to complex geodesics. In the present article we show that the same property holds for a three-point Pick problem on polydiscs, i.e. it may be expressed it in terms of three-complex geodesics. Using this idea we are able to solve that problem obtaining formulas and a uniqueness theorem for solutions of extremal problems. In particular, we determine a class of rational inner functions interpolating that problem. Possible extensions and further investigations are also discussed.

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Lukasz Kosinski. 2015-03-10. Three-point Nevanlinna Pick problem in the polydisc. https://arxiv.org/abs/1503.03091

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