article

Title: Self-mappings of the quaternionic unit ball: multiplier properties, the Schwarz-Pick inequality, and the Nevanlinna-Pick interpolation problem

Authors: Irene Sabadini, Daniel Alpay, Vladimir Bolotnikov and Fabrizio Colombo

Issue: Volume 64 (2015), Issue 1, 151-180

Abstract:

$We study several aspects concerning slice regular functions mapping the quaternionic open unit ball $\mathbb{B}$ into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space $\mathrm{H}^2(\mathbb{B})$. In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.$