A Cauchy kernel for slice regular functions |
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Authors: | Fabrizio Colombo Graziano Gentili Irene Sabadini |
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Institution: | 1.Dipartimento di Matematica,Politecnico di Milano,Milano,Italy;2.Dipartimento di Matematica,Università di Firenze,Firenze,Italy |
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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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Keywords: | |
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