Habetha, Klaus Einige geometrische Aussagen in der Cliffordalgebra und die Subharmonizität des Betrages einer regulären Funktion. (German) Zbl 0569.31003 Mathematica, Festschr. E. Mohr zum 75. Geburtstag, 79-93 (1985). [For the entire collection see Zbl 0555.00001.] Let G be open in \({\mathbb{R}}^{n+1}\) and let f be defined in G and taking values in the Clifford algebra \(C_ n({\mathbb{R}})\). Such a function f is called left-regular or left-monogenic in G if f is \(C^ 1\) in G and satisfies \(Df=0\) in G, where D is the generalized Cauchy-Riemann operator \(D=\sum^{m}_{i=0}e_ i\partial_{x_ i}\). A direct proof is given of the property that for a regular function f, \(| f|^ p\) is subharmonic for \(p\geq 1-1/n,\) this bound for p being sharp. The proof is based upon two lemmata about geometric properties of the Clifford algebra. Reviewer: F.Brackx MSC: 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 30G35 Functions of hypercomplex variables and generalized variables 15A66 Clifford algebras, spinors Keywords:Clifford algebra; left-regular; left-monogenic; generalized Cauchy- Riemann operator; subharmonic Citations:Zbl 0555.00001 PDFBibTeX XML