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Extensions of Clifford analysis to complex, finite dimensional, associative algebras with identity. (English) Zbl 0557.30043

Functions are considered, taking values in a complex, finite dimensional, associative algebra with identity and defined on subdomains of a complex subspace of this algebra, which are nullsolutions of a first order, homogeneous, elliptic operator with constant coefficients.
The results, including a generalized Cauchy theorem, homogeneous polynomials, Taylor expansion, Cauchy-Kowalewski extension theorem, parallel those of Clifford analysis, where the functions take values in a Clifford algebra.
Reviewer: F.Brackx

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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