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arXiv · 0708.3595

Slice monogenic functions

F. Colombo·I. Sabadini·D. C. Struppa
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Abstract

In this paper we offer a definition of monogenicity for functions defined on $\rr^{n+1}$ with values in the Clifford algebra $\rr_n$ following an idea inspired by the recent papers \cite{gs}, \cite{advances}. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra $\rr_n$. We will prove a Cauchy integral formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials and power series.

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F. Colombo, I. Sabadini, D. C. Struppa. 2008-01-25. Slice monogenic functions. https://arxiv.org/abs/0708.3595

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