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functions of one hypercomplex variable

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Division algebras of slice functions
Part of
Riccardo Ghiloni, Alessandro Perotti, Caterina Stoppato
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 4 / August 2020

Published online by Cambridge University Press:

15 March 2019, pp. 2055-2082

Print publication:

August 2020
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This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem.