
TL;DR
This paper explores the properties of slice Fueter-regular functions over octonions, showing they are standard slice functions with holomorphic-like features, and introduces operators to characterize them through differential systems.
Contribution
It demonstrates that slice Fueter-regular functions are standard slice functions with holomorphic properties and introduces global operators to characterize them via differential systems.
Findings
Slice Fueter-regular functions are standard slice functions with holomorphic properties.
They possess Cauchy integral formulas, series expansions, and maximum modulus principles.
The paper introduces operators to characterize these functions through second order differential systems.
Abstract
Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra , recently introduced by M. Jin, G. Ren and I. Sabadini. A function is called (quaternionic) slice Fueter-regular if, given any quaternionic subalgebra of generated by a pair of orthogonal imaginary units and ( is a `quaternionic slice' of ), the restriction of to belongs to the kernel of the corresponding Cauchy-Riemann-Fueter operator . The goal of this paper is to show that slice Fueter-regular functions are standard…
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