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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

Citations:

Zbl 0555.00001