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Three-point Nevanlinna Pick problem in the polydisc
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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