Nevanlinna-Pick Families and Singular Rational Varieties

Kenneth R. Davidson, Eli Shamovich

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

Abstract

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
Pages129-145
Number of pages17
DOIs
StatePublished - 1 Jan 2020

Publication series

NameOperator Theory: Advances and Applications
Volume278
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

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