Multipoint Schwarz-Pick Lemma for the quaternionic case

Abstract

Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz-Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz-Pick Lemma, in the context of the theory of slice regular functions. As applications, we obtain quaternionic Dieudonné and Goluzin estimates. Finally, an algorithm for the construction of (Nevanlinna-Pick) interpolating slice regular functions with real nodes is provided as a byproduct of the quaternionic multipoint Schwarz-Pick Lemma.

To appear in The Journal of Geometric Analysis, final version, 32 pages

References in corpus (6)

• Regular Moebius transformations of the space of quaternions
• The Schwarz-Pick lemma for slice regular functions
• Regular vs. classical Möbius transformations of the quaternionic unit ball
• On a class of orientation-preserving maps of ${\mathbb{R}}^4$
• Landau's theorem for slice regular functions on the quaternionic unit ball
• Log-biharmonicity and a Jensen formula in the space of quaternions