Monogenic differential calculus. (English) Zbl 0736.30034
In this rich and interesting paper the author considers differential forms with values in a Clifford algebra and the related Dirac operator. He establishes a Cauchy integral formula for monogenic differential forms which leads to formulas for nonintersecting cycles which turn out to be the respective winding numbers. This is applied to the study of cohomology theory and duals of spaces of monogenic differential forms. From the latter a general residue theory in Euclidean space is developped. The results include those of the author in Proc. R. Ir. Acad. 84, 87-109 (1984; Zbl 0545.30037).
Reviewer: K.Habetha (Aachen)
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 46F15 | Hyperfunctions, analytic functionals |
| 55M25 | Degree, winding number |
| 58A12 | de Rham theory in global analysis |
| 58A14 | Hodge theory in global analysis |
References:
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