Hilbert function spaces and the Nevanlinna–Pick problem on the polydisc

In [4], Agler and McCarthy (2005) 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 problem on Dn 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.