Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra \\mathbb{O} \\mathbb{O} , recently introduced by M. Jin, G
Alpay, D., Diki, K., Sabadini, I.: On the global operator and Fueter mapping theorem for slice polyanalytic functions. Anal. Appl. (Singap.) 19(6), 941–964 (2021) Article MathSciNet Google Scholar Altavilla, A.: Twistor interpretation of slice regular functions. J. Geom. Phys. 12...
functions. The class of these functions includes both the theory ofmonogenic functions and of slice monogenic functions with values in a Clif f ordalgebra. In this paper, we prove a version of the Fueter-Sce theorem in this newsetting, which allows to construct monogenic functions in higher ...
In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the ...
In this paper we develop a theory of slice regular functions on a real alternative algebra A. Our approach is based on a well-known Fueter's construction. Two recent function theories can be included in our general theory: the one of slice regular functions of a quaternionic or octonionic ...
On the global operator and Fueter mapping theorem for slice polyanalytic functionsdoi:10.1142/S0219530520500189Daniel AlpayKamal DikiIrene SabadiniWorld Scientific Publishing Company
functions is a natural generalization of that of holomorphic functions of one complex variable to the setting of quaternions, octonions, paravectors in Clifford algebras, and more generally quadratic cones of real alternative algebras, in virtue of a slight modification of a well-known Fueter ...
The functions g1 := − 1 4 (xg) and g2 = − 1 4 g are axially monogenic on thanks to Fueter's Theorem 1(2b). To conclude the existence part of the proof it remains to show that there exists a slice-regular primitive of f on . Let {e0, e1, e2, e3} be a real basis ...
Genchev, T.G.: Paley–Wiener type theorems for functions in Bergman spaces over tube domains. J. Math. Anal. Appl. 118(4), 496–501 (1986) Article MathSciNet MATH Google Scholar Gentili, G., Struppa, D.C.: A new approach to Cullen-regular functions of a quaternionic variable. C...
This last property relates the operator with the recent theory of slice monogenic and slice regular functions of a Clifford variable.doi:10.1007/978-88-470-2445-8_6Alessandro PerottiSpringer MilanA. Perotti, Fueter regularity and slice regularity: meeting points for two function theories, Advances ...