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.
A Cauchy kernel for slice regular functions / Colombo, Fabrizio; Gentili, Graziano; Sabadini, Irene. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - STAMPA. - 37:(2010), pp. 361-378. [10.1007/s10455-009-9191-7]
A Cauchy kernel for slice regular functions
GENTILI, GRAZIANO;
2010
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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