Abstract
An index formula is defined and it is used to derive a sufficiently general Cauchy integral formula for regular mappings in the euclidean Hurwitz pairs theory. Such a formula is a generalisation of the standard one known from the complex analysis.
The results obtained here are homogeneous dimensional and given as simple expressions in terms of the Hurwitz multiplication. They are generalizations of results stablished by Bartik, Ferreira, Markl and Souček [1] in the complex-quaternionic case and are related to analogous theorems of Brackx, Delanghe and Sommen [2] and Hestenes [3] for monogenic functions.
This work is partially supported by CONACYT grant A128CCOE890497 (MT-2)
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References
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Królikowski, W., Ramirez de Arellano, E. (1992). Fueter-Hurwitz Regular mappings and an integral representation. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_24
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DOI: https://doi.org/10.1007/978-94-015-8090-8_24
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