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arXiv · 1812.07133

A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics

Daniel Alpay·Ismael L. Paiva·Daniele C. Struppa
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Abstract

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter expansions, Gleason's problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.

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Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa. 2018-12-18. A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics. https://arxiv.org/abs/1812.07133

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