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A Cauchy kernel for slice regular functions

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Abstract

In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133, Milano, Italy

    Fabrizio Colombo & Irene Sabadini

  2. Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67 A, Firenze, Italy

    Graziano Gentili

Authors
  1. Fabrizio Colombo
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  2. Graziano Gentili
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  3. Irene Sabadini
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Correspondence to Irene Sabadini.

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Colombo, F., Gentili, G. & Sabadini, I. A Cauchy kernel for slice regular functions. Ann Glob Anal Geom 37, 361–378 (2010). https://doi.org/10.1007/s10455-009-9191-7

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  • DOI: https://doi.org/10.1007/s10455-009-9191-7

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