2023/12/15 by Bisi, Cinzia, Cordella, Davide
#30G35 #Complex Variables (math.CV) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2312.09664
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.