On a Generalization of Fueter’s Theorem

Franciscus Sommen

doi:10.4171/zaa/988

JournalszaaVol. 19, No. 4pp. 899–902

On a Generalization of Fueter’s Theorem

Franciscus Sommen
Universiteit Gent, Belgium

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Abstract

In this paper we discuss a generalization of Fueter’s theorem which states that whenever $f (x_{0}, x)$ is holomorphic in $x_{0} + x$ , then it satisfies $D ? f = 0, D = \partial_{x_{0}} + i \partial_{x_{1}} + j \partial_{x_{2}} + k \partial_{x_{3}}$ being the Fueter operator.

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Franciscus Sommen, On a Generalization of Fueter’s Theorem. Z. Anal. Anwend. 19 (2000), no. 4, pp. 899–902

DOI 10.4171/ZAA/988