Slice Fueter-Regular Functions

Slice Fueter-regular functions, originally called slice Dirac-regular are generalized holomorphic functions defined over the octonion algebra \({\mathbb {O}}\), recently introduced by M. Jin, G. Ren and I. Sabadini. A function \(f:\Omega _D\subset {\mathbb {O}}\rightarrow {O}}\) is (quaternionic) if, given any quaternionic subalgebra {H}}_{\mathbb {I}}\) of generated a pair {I}}=(I,J)\) orthogonal imaginary units I J (\({\mathbb ‘quaternionic slice’ {O}}\)), restriction f to belongs kernel corresponding Cauchy–Riemann–Fueter operator \(\frac{\partial }{\partial x_0}+I\frac{\partial x_1}+J\frac{\partial x_2}+(IJ)\frac{\partial x_3}\). The goal this paper show that standard (complex) whose stem satisfy Vekua system having exactly same form one characterizing axially monogenic degree zero. mentioned sliceness able reveal their ‘holomorphic nature’: have Cauchy integral formulas, Taylor Laurent series expansions, version Maximum Modulus Principle, each these properties global in sense it true on genuine 8-dimesional domains {O}}\). real analytic. Furthermore, we introduce concepts spherical Dirac \(\Gamma \) Fueter \({\overline{\vartheta }}_F\) octonions, which allow characterize as \({\mathscr {C}}^2\)-functions satisfying second order differential associated with \).