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<p>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.</p>

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Multipoint Schwarz–Pick Lemma for the Quaternionic Case

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月31日

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  • Cinzia Bisi,
  • Davide Cordella

摘要

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.