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• W3168925967 abstract "Slice Fueter-regular functions, originally called slice Dirac-regular functions, 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 _Dsubset {mathbb {O}}rightarrow {mathbb {O}}) is called (quaternionic) slice Fueter-regular if, given any quaternionic subalgebra ({mathbb {H}}_{mathbb {I}}) of ({mathbb {O}}) generated by a pair ({mathbb {I}}=(I,J)) of orthogonal imaginary units I and J (({mathbb {H}}_{mathbb {I}}) is a ‘quaternionic slice’ of ({mathbb {O}})), the restriction of f to ({mathbb {H}}_{mathbb {I}}) belongs to the kernel of the corresponding Cauchy–Riemann–Fueter operator (frac{partial }{partial x_0}+Ifrac{partial }{partial x_1}+Jfrac{partial }{partial x_2}+(IJ)frac{partial }{partial x_3}). The goal of this paper is to show that slice Fueter-regular functions are standard (complex) slice functions, whose stem functions satisfy a Vekua system having exactly the same form of the one characterizing axially monogenic functions of degree zero. The mentioned standard sliceness of slice Fueter-regular functions is able to reveal their ‘holomorphic nature’: slice Fueter-regular functions have Cauchy integral formulas, Taylor and Laurent series expansions, and a version of Maximum Modulus Principle, and each of these properties is global in the sense that it is true on genuine 8-dimesional domains of ({mathbb {O}}). Slice Fueter-regular functions are real analytic. Furthermore, we introduce the global concepts of spherical Dirac operator (Gamma ) and of slice Fueter operator ({overline{vartheta }}_F) over octonions, which allow to characterize the slice Fueter-regular functions as the ({mathscr {C}}^2)-functions in the kernel of ({overline{vartheta }}_F) satisfying a second order differential system associated with (Gamma )." @default.
• W3168925967 created "2021-06-22" @default.
• W3168925967 creator A5028797291 @default.
• W3168925967 date "2021-06-14" @default.
• W3168925967 modified "2023-09-24" @default.
• W3168925967 title "Slice Fueter-Regular Functions" @default.
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• W3168925967 doi "https://doi.org/10.1007/s12220-021-00709-x" @default.
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