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Dual slice functions and dual quaternionic polynomials
Abstract
This work constructs a new function class over the algebra of dual quaternions: dual slice functions, which include one-sided dual quaternionic polynomials. The peculiar properties of dual slice functions therefore provide new tools to understand factorization of dual quaternionic polynomials, which was extensively studied in recent years for its applications to mechanism science. Dual slice functions are strictly related to the well-established theory of slice and slice regular functions over quaternions and dual quaternions.
Related
- A connection between quaternionic slice regular and Fueter hyperholormorphic functions
- A four-dimensional residue calculus for quaternionic slice regular functions
- Classifying Slice-Regular Polynomials via Group Actions on the Twistor Space
- Radial reduction, spherical splitting and root counts for two-sided quaternionic polynomials
- Quaternionic Möbius invariant Laplacian and quaternionic Möbius harmonic functions on the unit ball
BibTeX
@misc{binosi2026dual,
title = {{Dual slice functions and dual quaternionic polynomials}},
author = {Giulio Binosi and Caterina Stoppato},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35518},
eprint = {2609.35518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35518},
}
RIS
TY - UNPB
TI - Dual slice functions and dual quaternionic polynomials
AU - Giulio Binosi
AU - Caterina Stoppato
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35518
UR - https://arxiv.org/abs/2609.35518
AB - This work constructs a new function class over the algebra of dual quaternions: dual slice functions, which include one-sided dual quaternionic polynomials. The peculiar properties of dual slice functions therefore provide new tools to understand factorization of dual quaternionic polynomials, which was extensively studied in recent years for its applications to mechanism science. Dual slice functions are strictly related to the well-established theory of slice and slice regular functions over quaternions and dual quaternions.
ER -