Three-point Nevanlinna Pick problem in the polydisc
Complex Variables
2015-03-12 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1503.03091,
title = {Three-point Nevanlinna Pick problem in the polydisc},
author = {Lukasz Kosinski},
journal= {arXiv preprint arXiv:1503.03091},
year = {2015}
}