Nevanlinna-Pick interpolation on distinguished varieties in the bidisk
arXiv:1009.4144 · doi:10.1016/j.jfa.2012.01.028
Abstract
This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.
31 pages. The question left open at the end of version 1 has been answered in the affirmative; see Theorem 1.12 and Corollary 1.13 in version 2
References in corpus (4)
Cited by in corpus (10)
- Distinguished Varieties Through the Berger--Coburn--Lebow Theorem
- Polynomials with no zeros on a face of the bidisk
- Level curve portraits of rational inner functions
- Function theory on quotient domains related to the polydisc
- Schwarz-Pick type inequalities from an operator theoretical point of view
- Distinguished varieties and the Nevanlinna-Pick interpolation problem on the symmetrized bidisk
- de Branges-Rovnyak spaces which are complete Nevanlinna-Pick spaces
- Lax-Halmos Type Theorems in H^p Spaces
- Invariance Under Bounded Analytic Functions
- Realizations via Preorderings with Application to the Schur Class