TY - CHAP

T1 - Nevanlinna-Pick Families and Singular Rational Varieties

AU - Davidson, Kenneth R.

AU - Shamovich, Eli

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85097680787&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-43380-2_7

DO - 10.1007/978-3-030-43380-2_7

M3 - Chapter

AN - SCOPUS:85097680787

T3 - Operator Theory: Advances and Applications

SP - 129

EP - 145

BT - Operator Theory

PB - Springer Science and Business Media Deutschland GmbH

ER -