On a Generalization of Fueter’s Theorem

  • Franciscus Sommen

    Universiteit Gent, Belgium


In this paper we discuss a generalization of Fueter’s theorem which states that whenever f(x0,x)f(x_0, x) is holomorphic in x0+xx_0+x, then it satisfies D?f=0,D=x0+ix1+jx2+kx3D?f = 0, D= \partial_{x_0} + i \partial_{x_1}+ j \partial_{x_2} + k \partial_{x_3} being the Fueter operator.

Cite this article

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

DOI 10.4171/ZAA/988