Nevanlinna-Pick Families and Singular Rational Varieties

Kenneth R. Davidson, Eli Shamovich

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The goal of this note is to apply ideas from commutative algebra (a.k.a. affine algebraic geometry) to the question of constrained Nevanlinna-Pick interpolation. More precisely, we consider subalgebras A⊂ ℂ[ z1, …, zd], such that the map from the affine space to the spectrum of A is an isomorphism except for finitely many points. Letting be the weak-∗ closure of A in ℳd —the multiplier algebra of the Drury-Arveson space. We provide a parametrization for the Nevanlinna-Pick family of Mk for k ≥ 1. In particular, when k = 1 the parameter space for the Nevanlinna-Pick family is the Picard group of A.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
StatePublished - 1 Jan 2020

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

ASJC Scopus subject areas

  • Analysis


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