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Extension problem for the generalized biregular functions in Clifford analysis. (English) Zbl 0786.30030

Let \(A\) be the Clifford algebra over \(\mathbb{R}^ m\) and \(f: G\to A\) be a generalized biregular function on the domain \(G\subset \mathbb{R}^{n+k}\), \(n,k<m\). The author studies an extension phenomenon when every generalized biregular function on an open neighbourhood of \(\partial G\) may be extended continuously in the whole of \(G\) as a generalized biregular function. In the case when \(G= G_ 1\times G_ 2\) and \(G_ 1\) and \(G_ 2\) are domains in \(\mathbb{R}^ n\) and \(\mathbb{R}^ k\) respectively, \(n,k<m\), he proves an anlogue of the Hartogs extension theorem from the theory of holomorphic functions of several complex variables.
Reviewer: M.Marinov (Sofia)

MSC:

30G35 Functions of hypercomplex variables and generalized variables
32S30 Deformations of complex singularities; vanishing cycles
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