Pick Interpolation for free holomorphic functions

Pick Interpolation for free holomorphic functions

Free Holomorphic Functions and Interpolation

In this paper we obtain a noncommutative multivariable analogue of the classical NevanlinnaPick interpolation problem for analytic functions with positive real parts on the open unit disc. Given a function f : Λ → C, where Λ is an arbitrary subset of the open unit ball Bn := {z ∈ Cn : ‖z‖ < 1}, we find necessary and sufficient conditions for the existence of a free holomorphic function g with c...

A Constrained Nevanlinna-pick Interpolation Problem for Matrix-valued Functions

Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the NevanlinnaPick interpolation problem on the unit disk with the additional restriction that the interpolant should have the value of its derivative at the origin equal to zero. This concrete mild generalization of the classical problem is prototypical of a number of...

Nevanlinna - Pick Interpolation For

We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...

Weak Conditions for Interpolation in Holomorphic Spaces

An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when 0 < p ≤ 1, of Fock-type when 0 < p ≤ 2, and of Bergman-type when 0 < p < ∞. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with...