4 papers · 1 filter
A manifold Fueter-Sce phenomenon in one hypercomplex variable
Riccardo Ghiloni, Caterina Stoppato
Fueter's theorem states, in modern terms, that the Laplacian maps slice-regular quaternionic functions into Fueter-regular functions with axial symmetry. This phenomenon is also pr…
A unified theory of regular functions of a hypercomplex variable
Riccardo Ghiloni, Caterina Stoppato
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of -regular functions. In the special case of quaternion-valued functions of one quate…
Quaternionic slice regularity beyond slice domains
Riccardo Ghiloni, Caterina Stoppato
After Gentili and Struppa introduced in 2006 the theory of quaternionic slice regular function, the theory has focused on functions on the so-called slice domains. The present work…
A unified notion of regularity in one hypercomplex variable
Riccardo Ghiloni, Caterina Stoppato
We define a very general notion of regularity for functions taking values in an alternative real -algebra. Over Clifford numbers, this notion subsumes the well-established notio…