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| Titel: |
Regular n-forms in clifford analysis their behavior under change of variables and their residues |
| Auteur: |
Zoll, Georg |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 11 (1989) nr. 1 pagina's 25-38 |
| Jaar: |
1989-02 |
| Inhoud: |
In the present paper we generalize the concept of holomorphic differential form by calling a Clifford algebra valued n-form (.) regular iff there are functions f.g which are left respectively right regular such that [image omitted] . These are the differential forms which occur in many generalizations of classical theorems to Clifford analysis. as e.g. Cauchy's theorem . More as theorem etc. {compare [4]). Nonetheless. this type of n-form has apparently not yet been investigated in its own right. We consider the question. under which transformations T of variables regular n-forms transform into regular n-forms, and essentially find this true iff T is a Mobius transformation. These may be described conveniently in terms of Clifford algebra (see [l]-[3]). We decompose Mobius transformations into reflections in hyperplanes or spheres, in a way which gives some geometric insight into the action of a Mobius transformation on [image omitted] . Furthermore we define the residue of a regular n-form in a point singularity. and give a residue theorem. As applications we explicitly figure out an integral over [image omitted] . and get a nice formula for the degree of a mapping (compare [7]).1 |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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