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Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc (1104.2533v2)
Published 13 Apr 2011 in math.FA and math.CV
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 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.