On the Fueter-Sce theorem for generalized partial-slice monogenic functions
Complex Variables
2024-10-30 v1
Abstract
In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both the theory of monogenic functions and of slice monogenic functions with values in a Clifford algebra. In this paper, we prove a version of the Fueter-Sce theorem in this new setting, which allows to construct monogenic functions in higher dimensions starting from generalized partial-slice monogenic functions. We also prove that an alternative construction can be obtained by using the dual Radon transform. To this end, we provide a study of the generalized CK-extension.
Cite
@article{arxiv.2311.12545,
title = {On the Fueter-Sce theorem for generalized partial-slice monogenic functions},
author = {Zhenghua Xu and Irene Sabadini},
journal= {arXiv preprint arXiv:2311.12545},
year = {2024}
}
Comments
23 pages. arXiv admin note: text overlap with arXiv:2309.03698