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On the Hausdorff Analyticity for Quaternion-Valued Functions

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Abstract

We consider the concept of the Hausdorff analyticity for functions ranged in real algebras and the corresponding notion of the Hausdorff derivative. Both apply to the real algebra \(\mathbb {H}\) of Hamilton’s quaternions. The main aim of the work is to compare them with the well-known classes of \(\mathbb {H}\)-valued functions which have their own definitions of the derivative.

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Authors and Affiliations

  1. Holon Institute of Technology, Holon, Israel

    M. E. Luna-Elizarrarás & M. Shapiro

  2. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine

    V. Shpakivskyi

Authors
  1. M. E. Luna-Elizarrarás
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  2. M. Shapiro
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  3. V. Shpakivskyi
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Correspondence to M. E. Luna-Elizarrarás.

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Communicated by Daniel Aron Alpay.

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Luna-Elizarrarás, M.E., Shapiro, M. & Shpakivskyi, V. On the Hausdorff Analyticity for Quaternion-Valued Functions. Complex Anal. Oper. Theory 13, 2863–2880 (2019). https://doi.org/10.1007/s11785-018-0856-8

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  • DOI: https://doi.org/10.1007/s11785-018-0856-8

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