Three-point Nevanlinna Pick problem in the polydisc

2015/03/10 by Łukasz Kosiński, Kosinski, Lukasz · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1503.03091

openalex publication_date 2015/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Coman conjecture for the bidisc

Cited by

• The uniqueness problem for the 3-point Nevanlinna-Pick extremal interpolation problem in the unit Euclidean ball Bd

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