zbMATH — the first resource for mathematics

A generalization of Fueter’s monogenic functions to fine domains. (English) Zbl 1133.30014
Čadek, Martin (ed.), The proceedings of the 25th winter school “Geometry and physics”, Srní, Czech Republic, January 15–22, 2006. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 79, 129-138 (2006).
The author proposes an extension of the complex analysis’ concept of finely holomorphic functions to the class of monogenics functions with values in the quaternionic algebra \(\mathbb{H}.\) Main results are Theorem 2 and 4, regarding equivalence statements between the proposed concept and finely harmonic/continuous properties of those functions.
For the entire collection see [Zbl 1103.53001].

30G35 Functions of hypercomplex variables and generalized variables
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31C40 Fine potential theory; fine properties of sets and functions