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Cauchy-Kowalewski theorems in Clifford analysis: A survey. (English) Zbl 0546.30036

The authors give a review of parts of Clifford analysis, a considerable part of this theory has been developed by themselves, more information can be found in their book [Clifford analysis (1982; Zbl 0529.30001)]. This interesting report surveys mostly theorems around the extension on an analytic function defined on an n-dimensional surface in \({\mathbb{R}}^{n+1}\) to a regular function in an open neighbourhood of this surface. That gives rise to the definition of a special product of Clifford valued regular functions, this product has been proved to be very useful. Another point is the maximal domain of convergence of a multiple power series within the Clifford theory.
Reviewer: K.Habetha

MSC:

30G35 Functions of hypercomplex variables and generalized variables
35A10 Cauchy-Kovalevskaya theorems
30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable

Citations:

Zbl 0529.30001
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