Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems

Cinzia Bisi; Joerg Winkelmann

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arXiv · 2609.06160

Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems

Cinzia Bisi·Joerg Winkelmann

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Abstract

Slice regular functions are a generalization of holomorphic functions where alternative real $*$-algebras are considered instead of the field of complex numbers. For such functions we show that zero sets and function values on suitable subsets may be prescribed. As a consequence, we show that for any axially symmetric domain there exist slice regular functions which (due to the nature of its zero set) can not be extended to a larger such domain.

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Cinzia Bisi, Joerg Winkelmann. 2026-09-05. Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems. https://arxiv.org/abs/2609.06160

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