Self-mappings of the quaternionic unit ball: multiplier properties, the Schwarz-Pick inequality, and the Nevanlinna-Pick interpolation problem Daniel AlpayVladimir BolotnikovFabrizio ColomboIrene Sabadini 30G3530E05.Nevanlinna-Pick interpolation problemslice regular functionscontractive multipliers 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. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5456 10.1512/iumj.2015.64.5456 en Indiana Univ. Math. J. 64 (2015) 151 - 180 state-of-the-art mathematics http://iumj.org/access/