Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bisi, Cinzia, Winkelmann, Joerg
Institution: University of Ferrara
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212061756