2026/07/21 by José Oscar González-Cervantes, Daniel González-Campos, Juan Bory-Reyes +1
#math.CV
This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator G, Fueter operator \mathcal D and Laplacian operator Δℝ4. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball \mathbb B4(0,1) given in terms of new series expansions of the functions.