Slice monogenic functions

Details Slice monogenic functions Slice monogenic functions

2007-08-27

arxiv.org/abs/0708.3595v2

Israel J. Math. 171 (2009), 385--403

Mathematics

Complex Variables

to appear in Israel Journal of Mathematics

Scientific paper

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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