Abstract
It is elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are left inverses to complex geodesics. In the present article, we show that the same property holds for a three-point Pick problem on polydiscs, that is, the solution may be expressed in terms of 3-complex geodesics. Using this idea, we are able to obtain formulas and a uniqueness theorem for solutions of extremal problems. In particular, we determine a class of rational inner functions that solve the interpolation problem. Possible extensions and further investigations are also discussed.
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