Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc
Functional Analysis
2011-05-04 v2 Complex Variables
Abstract
In the paper `Distinguished Varieties,' Agler and McCarthy used Hilbert function spaces to study the uniqueness properties of the Nevanlinna-Pick problem on the bidisc. In this work we give a geometric procedure for constructing a Nevanlinna-Pick problems on D^n with a specified set of uniqueness. On the way to establishing this procedure, we prove a result about Hilbert function spaces and partially answer a question posed by Agler and McCarthy.
Keywords
Cite
@article{arxiv.1104.2533,
title = {Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc},
author = {David Scheinker},
journal= {arXiv preprint arXiv:1104.2533},
year = {2011}
}
Comments
The exposition and organization of the paper were revised in the second version. Neither the results, nor the proofs have been substantively altered