Abstract
In this paper the author is presenting a theory of functions on complex ternary algebras. The theory developed here is a particular case of the more general case discussed in a volume the author is preparing in collaboration with A. Vajiac and a continuation of the real ternary case developed in Alpay et al. (Adv Appl Clifford Algebr 28:1–16, 2018). The complex ternary algebra has a dual nature: on one side, it is a one–dimensional (one ternary variable) theory generated by an element that cubes to ± 1, on the other it behaves as a theory of one bicomplex variable and one complex variable entangled by algebra relations.
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Acknowledgements
Many thanks to my best friend and collaborator Adrian Vajiac for our numerous discussions on everything hypercomplex. Without his unwavering support this work would not have seen the light of day.
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Vajiac, M.B. (2021). Complex Ternary Analysis and Applications. In: Alpay, D., Peretz, R., Shoikhet, D., Vajiac, M.B. (eds) New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative. Operator Theory: Advances and Applications(), vol 286. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-76473-9_12
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