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 -