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On the Slice Regular Schwarz Derivative

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Abstract

The aim of this paper is to introduce, in the context of slice regular functions, three notions of the quaternionic Schwarz derivative with their the basic properties: the characterization of zeros, the conformal covariant property and the conformal invariant property. These concepts mimic the structure of the complex Schwarz derivative which is a differential operator with several properties and applications. Particularly, one of these operators is curiously related to the generalization of the schwarzian derivative over vector spaces given by Ryan (Ann Pol Math 57:29–44, 1992).

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Authors and Affiliations

  1. Departamento de Matemáticas, E.S.F.M. del I.P.N., 07338, Mexico, DF, Mexico

    J. Oscar González-Cervantes

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  1. J. Oscar González-Cervantes
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Correspondence to J. Oscar González-Cervantes.

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Communicated by Uwe Kaehler

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This work was partial supported by CONACYT.

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González-Cervantes, J.O. On the Slice Regular Schwarz Derivative. Adv. Appl. Clifford Algebras 29, 82 (2019). https://doi.org/10.1007/s00006-019-1004-x

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  • DOI: https://doi.org/10.1007/s00006-019-1004-x

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