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<p>We continue our investigations of the local properties of entire slice regular functions of quaternionic variable. For this class of functions, we introduce the notion of index. The boundedness of index is characterized in terms of the local behavior of the maximum modulus of slice derivative on certain discs. The corresponding maximum is uniformly estimated by the value of the modulus of slice derivative at the center of the disc. The presented results are quaternionic generalizations of the well-known Fricke theorems for entire functions of complex variable.</p>

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Slice Entire Functions of the Quaternionic Variable of Bounded Index

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Vita Baksa,
  • Andriy Bandura,
  • Oleh Skaskiv

摘要

We continue our investigations of the local properties of entire slice regular functions of quaternionic variable. For this class of functions, we introduce the notion of index. The boundedness of index is characterized in terms of the local behavior of the maximum modulus of slice derivative on certain discs. The corresponding maximum is uniformly estimated by the value of the modulus of slice derivative at the center of the disc. The presented results are quaternionic generalizations of the well-known Fricke theorems for entire functions of complex variable.