Ryan, John Extensions of Clifford analysis to complex, finite dimensional, associative algebras with identity. (English) Zbl 0557.30043 Proc. R. Ir. Acad., Sect. A 84, 37-50 (1984). 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 Cited in 3 Documents MSC: 30G35 Functions of hypercomplex variables and generalized variables Keywords:Cauchy-Kowalewski extension; Clifford analysis; Clifford algebra PDFBibTeX XMLCite \textit{J. Ryan}, Proc. R. Ir. Acad., Sect. A 84, 37--50 (1984; Zbl 0557.30043)