Abstract
We give a survey about the development of an elementary concept of hypercomplex differentiable A-valued functions defined in open subsets Ω of R m+1, whereby A is a Clifford algebra over the field of real numbers. Using a different from the usual one hypercomplex structure of R m+1 we get by this way a natural generalization of the Cauchy approach to monogenic functions which seems to be not possible so far. Exemplary this concept applies to transfer important properties of holomorphic functions in the plane. The results are of wide formal uniformity with the theory of functions of several complex variables.
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© 1993 Kluwer Academic Publishers
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Malonek, H.R. (1993). Hypercomplex Differentiabilty and its Applications. In: Brackx, F., Delanghe, R., Serras, H. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2006-7_17
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DOI: https://doi.org/10.1007/978-94-011-2006-7_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-2347-1
Online ISBN: 978-94-011-2006-7
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