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

By David Scheinker

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.Comment: The exposition and organization of the paper were revised in the second version. Neither the results, nor the proofs have been substantively altere

Topics: Mathematics - Functional Analysis, Mathematics - Complex Variables, 46E20, 46E22, 32A07, 47B32, 30J05
Year: 2011
OAI identifier: oai:arXiv.org:1104.2533
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