Agler Interpolation Families of Kernels

Complete Nevanlinna-Pick Kernels

We give a new treatment of Quiggin’s and McCullough’s characterization of complete Nevanlinna-Pick kernels. We show that a kernel has the matrix-valued NevanlinnaPick property if and only if it has the vector-valued Nevanlinna-Pick property. We give a representation of all complete Nevanlinna-Pick kernels, and show that they are all restrictions of a universal complete Nevanlinna-Pick kernel.

Pick Interpolation for free holomorphic functions

A tangential interpolation problem on the distinguished boundary of the polydisk for the Schur–Agler class

We study a tangential interpolation problem with an arbitrary set of interpolating points on the distinguished boundary of the unit polydisk for Schur–Agler class. The description of all solutions is parametrized in terms of a linear fractional transformation.  2002 Elsevier Science (USA). All rights reserved.

An Improved Julia-caratheodory Theorem for Schur-agler Mappings of the Unit Ball

We adapt Sarason’s proof of the Julia-Caratheodory theorem to the class of Schur-Agler mappings of the unit ball, obtaining a strengthened form of this theorem. In particular those quantities which appear in the classical theorem and depend only on the component of the mapping in the complex normal direction have K-limits (not just restricted K-limits) at the boundary. Let B denote the open uni...

Test Functions in Constrained Interpolation

We give a set of test functions for the interpolation problem on H 1 , the constrained interpolation problem studied byDavidson, Paulsen, Raghupathi and Singh. We show that this set of test functions is minimal. 1. Background and Introduction There has been increased interest in constrained interpolation problems recently. Theseproblems havemany of the unusual characteristics of harder interpol...